This may be not the answer you are looking for but I will approach the problem from a worldbuilding perspective, as I'm too rusty and there are chemistry and biology SE's. Plus, there is a big hole in your plot which I would like to address.
You may be heading in the wrong direction
When we talk about high metabolic rates, the first thing which comes to mind is birds. Google for "bird metabolic rates", and sure enough there are different studies that investigate different aspects of avian metabolism, including the factors which affect it to be higher, among others.
On top of my search results, I see Avian Energy Balance & Thermoregulation, which is simple enough and can be useful for the case. Let it be our source of data.
Birds have high basal metabolic rates & so use energy at high rates. Among birds, songbirds (passerines) tend to have higher basal metabolic rates than nonpasserines. And, of course, the smallest birds, hummingbirds, have the highest basal metabolic rates of all birds. In general, basal metabolic rate (or BMR) is related to mass, with larger birds expending less energy per unit weight than smaller birds.
As you can see, small birds have 10-30 times faster metabolic rates than humans. So if you dive deeper into the topic of what makes them be so energetic, you can draw scientifically accurate reasons for your artificial soldiers or creatures.
Some Fundamentals
To be more specific to your question, you are missing some vital parts which have a greater impact.
Let's look at Krebs cycle
The details are not important for us, but the overall picture is relevant. Observe that there are 10-11 reactions at least - and each of those can be a bottleneck. So your most significant mistake is to consider that ATP part is the only source of the bottleneck, and if one looks at it from the perspective of excursion power, it may look true but it's more like burst power at best. More important is how fast AMP is restored to ATP and that is defined by Krebs and(or) others.
As we saw on Hummingbird, the difference it can make is over the order of magnitude of continuous power. And if there is need for more burst power, changes in concentrations of ATP can have more impact than Ap4 or Ap5, which may or may not bring +20% of something, when a simple 2 times increase of concentration brings you +100%.
Reactions of metabolic cycles have low potential barriers (not sure how it is called in English, energy to initiate the reaction is low, relatively) and for this reason, small changes in temperatures have a good impact on the intensity of the reaction - but it has to be understood that it is a function of many factors, and there is a limit to how far we can ride the vehicle.
Difference between Artificial and Natural
Are birds fundamentally different from others since they have metabolic rates higher by an order of magnitude? Unless there is data indicating otherwise, we probably have to stick to no, because of evolution and all that.
With naturally evolved species we have to understand that metabolic rate is not the goal, survival is. Therefore, those rates are a tool and are a function of means, environment, and seasonal changes in which the birds have to survive. And burning at max is not necessarily beneficial to survival.
So naturally evolving species have to compromise. Even a 0.01% improvement that shines in some specific situation that doesn't necessarily occur all the time, can be beneficial over generations and population numbers.
Hence the food sources, nutrition values, scaling down the concentrations of enzymes that work in metabolic cycles, etc.
Synthetic life does not have most of those restrictions, so its goal is defined by those who create them and it probably isn't survival in a natural environment. So we can create a big body (at least by mass) species with the metabolic rate of a hummingbird, say as big as an elephant for example. From the perspective of natural survival, it would be insane just by size and accessibility and the extent of the area/territory which is needed to feed such a creature. But for us, it is a lesser problem as we can probably attach some energy converter and supply that creature with the energy it needs.
For our 5000kg elephant hummingbird it will be 390kw per organism. Quite a lot actually, it can be directly compared with some lower-tech versions of combustion engines. Inefficiencies aside, injecting the energy to our elephant as waste heat from that process can be kept external, but still, we hit some physical limitations which synthetic organisms are subject to, which we have to solve through the design of such an organism - but in the shape of an elephant, it will be quite hard to dissipate 390kw. This again depends on the technology available - we still can solve that by an external embedded cooling system, but again such things will obviously be subject to physics.
Just a side note about how much 390kw is in nature. 1 tonne of dry grass/straw contains about 3900kwh of energy. Coincidentally, that number is quite close to what we need. So our elephant hummingbird needs to digest at least 100kg of dry grass per hour and about 2.4 tons of it per day. Again, coincidentally that amount of grass grows on 100x100m area (yields are 1-3t per hectare). Dino descendant is that u?
By itself, it looks doable, but they have to procreate, and that occupies some common area, causes competition, etc. Again possible, I guess in dino days things were good enough to allow that, but we all know what happened - the environment was shaken and they didn't make it.
As grass is not necessarily the best food source there is - efficiency-wise and factoring in speed of digestion - actual numbers including those factors will bring a few times higher consumption rates and therefore area necessary. Since grass grows for 3-4 months, a season - the total area needed to feed one organism will be a few square km per creature.
Energy dissipation depends on the surface area, so a flat body plan can dissipate 390kw better - idk probably a centipede?
Connected google overlord just to check and they have answered:
How much do elephants eat and drink per day?
Adult elephants can eat between 200-600 pounds of food a day. As herbivores, elephants consume grasses, tree foliage, bark, twigs, and other vegetation daily. Elephants can also drink up to 50 gallons of water a day about as much as a standard bathtub holds.
Hence, I have to conclude that I didn't shoot high enough with our elephant hummingbird, they still do not put nature to shame.
Summing Up
In general, limits of what's already available in nature are higher than what we observe typically, and those limits encompass low and high extremes. Biological systems use the building blocks available to adjust themselves to the conditions they survive in.
Synthetics are freer from evolutionary restrictions, so we can have performances higher than anything that is typical in nature, combining the best from all different species. For example, humans do not have the best muscle tissues, there are creatures that have more robust muscles as tensile strength goes (and that can mean more strength in a smaller package). However, a trained human is a top predator because they can exhaust any creature (land ones I guess, so again it mammal vs mammal) by not stopping in pursuit of them over days. Sure, it's more from our hunter-gatherer times, not many tribes of today can do that(my guess), but there are some which can still do that(seen about them).
So the whole biological system/library is our lego blocks, we are more restricted by our knowledge and how much we have read in that library. There is still a long way to go, but in the future, we can imagine it not being as big of a limitation as it is today. Hopefully, we won't burn it down like The Great Library of Alexandria before we do read it, lol.
But also, physics trumps all the systems, including biological ones, so do not forget physics is king.
Things I forgot.
With metabolic festivities, I totally forgot about the respiration problem, and more like blood capacities specifically. But respiration limitations is probably out of the scope of the question, but they also have some science behind it and works studies on that subject, and after all it still connected to ATP. It's more archeological as of today's, biological differences environments in previous eras. So it may have the sense to dig in that direction, however, it may be less applicable to synths as we may address this and other problems in ways not accessible to biological systems, which I forgot to mention as well, did I? hm, I forgot ...