only if you account for the magic and for a lack of competition. At least when it comes to the runners.
Let me start by saying something sad: while we have cases in which caterpillars did evolve into predators, they're not exactly the most suitable for the job. It is true that Hawaiian caterpillars have evolved into fearsome and successful predators, but something that must be addressed is how they're exclusive to Hawaii, a place where other ambush predators such as the praying mantis were completely absent and the niche completely vacant. We have info that they can become successful predators, but there are some things we need to address on caterpillars specifically that stack against them in some of your creatures:
they're larvae. At the end of the day, every caterpillar has 2 simple goals: survive and eat. If they don't survive they can't eat, and if they can't eat they can't accumulate enough energy to grow and eventually metamorphose into their adult stage. Essentially, larvae have an extra problem when it comes to reaching adulthood that one might call the drawback of them not needing to compete with adults for resources: they need a lot of energy because they'll necessarily need to enter a stage of absolute lack of movement and intense energy consumption. This energy cost is something we already see in many predators, which need to make sure the amount of energy they waste hunting is not higher than the amount they get from their successful hunts. This energy cost applied to a larval stage might be (although it's not exactly stated as a fact) a strong reason for why all examples of strictly carnivorous caterpillars we have are all ambush predators which hunt by standing almost completely still until prey comes along.
they're not fast. The natural anatomy of a caterpillar, which is itself the larva of a butterfly or moth, is not built for speed at all. Their movements are mostly reliant on them ondulating their bodies, and the fastest examples come from caterpillars which have less legs, relying on a more extreme ondulating movement to go around, and still they're not nearly as fast, being 38 mm long and reaching top speeds of 5 cms/s, 5 times faster than your average caterpillar. To put it in perspective, if they were magically scaled up to be 3 meters long and kept roughly the same max speed in relation to their body length, they'd clock in at a total of... Approximately 4 meters per second. Your average human can reach sprinting speeds of 5,5 m/s, meaning those caterpillars aren't outrunning anything. This makes sense, as the majority of caterpillars don't need to be fast, and even those that actually act as predators only evolved to be able to strike fast, being otherwise stationary and not exactly nimble.
These 2 facts alone already make the path for the runner group very bumpy. Pursuing prey requires a lot of energy and requires an animal to be both speedy and strong enough to overpower whatever it managed to outrun. Cheetahs for example have their hunting success rate at a respectable 58%. Problems: their hunting method demands absurd amounts of energy and extreme adaptations for speed, both of which are pretty bad things of you're but a larval stage that has the primary objective of storing as much energy as possible and is yet to become a fertile adult.
In addition to the problems of drastic anatomical changes just so these larvae can make the cut for pursuit predators, we also have one final problem which also applies to the ambushers: competition. It's no accident that we only observe carnivorous caterpillars in an ecosystem where mantises do not exist. Truth is that when a niche is already occupied by a creature, natural selection tends to be stacked against any other competitors that aren't already adapted for said niche. Think of the following example: a class of 5 year olds decide they want to eat cookies, but to get those cookies they need to be able to reach the table where they're placed first in an all out sprint. Now this wouldn't be a problem, if they weren't competing with another class composed entirely of adult clones of Usain bolt who have no intention of sharing any cookies. If left unattended, these kids would need to either eat something else or starve to death. Your caterpillars are at a similar situation, where their body plan and overall lifecycle as is are already against them. Couple that with the presence of another predator that's more adapted for sprinting and they're completely off the game.
For these reasons I'd say the runner group is very unlikely. They'd need to suffer heavy adaptations just to fit in the niche properly and they'd most likely still be in a situation where they'd be easily outcompeted and driven to extinction by other species much more suited for such niches, like ordinary big cats and wild dogs (fun fact: the African wild dogs have a success rate of 85%). The only way I see this working would be them existing in a place with no competition and a lot of prey items with very little ability to deter a pursuit predator, and even then to become decent enough you'd basically need them to become something like a centipede, but with a lot less legs.
AS for the ambush group...yep, pretty plausible. We already know that this hunting strategy is viable for a caterpillar and doesn't require nearly as many changes to work well (out of all species of the group that includes all carnivorous caterpillars we know of, only 2 are herbivores, which is an indicator that this lifestyle is easily viable) Carnivorous caterpillars as they come already use their spiked frontal appendages to immobilize and subdue prey and eat them alive, so essentially they already work as both grabbers and smashers up to a point, the main difference being how hard they hit their prey upon striking.
Spitters also have real world counterparts up to a point. Another group of Hawaiian caterpillars use their silk to stick sleeping snails to leaves and prevent them from escaping. Once they wake up and try to escape, the caterpillar waits until it gives up and hides again, at which point it crawls into the shell and eats it alive. velvet worms meanwhile , while not caterpillars, are known to shoot a special quick hardening slime at prey, at which point it injects it with digestive juices and drinks the thing up.
Your reelers in particular sound like a tough concept to implement with a caterpillar though. Bolas spiders rely on silk lines with a drop of sticky "glue" at the tip to hunt the moths they eat (they also make use of pheromones to trick the moths into approaching it for a seemingly sexy time, except they don't exactly experience being in a romantic diner, just being a dinner). To make it work your reeler would need a similar method, with the main difference being that it would also need muscles capable of shooting that line and proper mouthparts for pulling the prey without accidentally biting the string off. They'd also need to worry about their prey being very much aware of what's going on and potentially getting free or even harming the predator unexpectedly. I'd say it'd be safer for your caterpillars to stick to the "restrain prey as they sleep" strategy, as it allows for less risks and doesn't require the caterpillar to need things such as venom nearly as much.
So for the classic summary: are they feasible? Not all of them. The runners seem to be pretty unlikely, as they're coming from something that can't waste a lot of energy, doesn't have a bodyplan or a metabolism very suitable for moving fast and would need drastic changes to their anatomy just to become viable, at which point they'd likely still need to be isolated from other predator groups and suffer a serious risk of extinction if they ever had to deal with exotic pursuit predators.
Your ambushers on the other hand are mostly both proven to be likely viable, as we already have fairly similar real life counterparts to these creatures, as well as examples of non-caterpillar species with similar strategies to what you want (the velvet worm being very close to what you want from the netters, its only sin being that it's not a caterpillar). The least viable I'd say would be the reeler caterpillar, since its hunting strategy is both fairly hard to pull out given the constraints of a caterpillar body plan and essentially gives whatever its trying to capture a heads up that it's in danger (your prey knowing it's been caught works better for spiders and silkworms because the prey normally can't do much to set itself free).
AS for improving the archetypes, I think I already said enough: fuse the reelers with the netters so you can get a caterpillar that shoots sticky silk strings at prey, with the main difference being making the silk stronger. That makes it so the caterpillar can safely restrain its prey from a distance approach the prey and eat it alive without needing strategies like melting it from the inside.
As for the runners: sorry, I looked at caterpillar speeds, how they move and what the fastest ones were, but I just couldn't manage to make it work in a satisfying way. Since you seemed to be already on a path to make them more similar to centipedes in general, I'd suggest making use of them instead, they're already competent speedy predators, with the scolopendra genus being naturally able to grow large (several species having individuals that can grow to over 20 cm long) and being deceptively fast and competent climbers which already give animals such as snakes, bats, rodents and birds a run for their money (also some feel very much at home swimming in the water),so their high mobility and speed could allow them to fit the role of stalkers without much problem. To give a better context for speed, the giant desert centipede can reach speeds of ~4 m/s and a maximum length of 20 cm, which means that a 3-meter long giant desert centipede magically scaled up would be able to reach bursts of over 200 km/h.
Finally, which of these caterpillars could prey on the leafmaw? Honestly, I'd dare to say all of them. You did a very good job at these to the point it turns out the concepts you want are already used by many successful predators. Combine those with how hard it is to poison a caterpillar (I found out recently that many caterpillar species are remarkably capable at resisting envenomation, due to how their nervous system is structured) and I could easily see any of your ambusher variants being capable of serving as predators to the leafmaws, the main constraint being whether they're big enough.