Is a species with high paternal parental investment feasible?
High paternal parental investment actually exists in many species. The term used for this kind of species is "pair bonding species", as opposed to "tournament species", but don't be mislead by the terminology - there is a cluster of behavior features found together in each of those two types of species, and making a pair bond is only one of the features in that cluster. In pair bonding species, the dads deliver a lot of care for the offspring. Here is a description of these features:
Sapolsky, Robert M. Behave: The biology of humans at our best and worst. Penguin, 2017.
It is unclear how these two opposing strategies get started within a species (and they are also just two ends of the spectrum - there are lots of intermediate cases, including us humans). But once you have a species where this is the case, it is a stable state - there is evolutionary pressure for the species to remain as it is, including the dad investment. For example:
- "Females select for: parenting skill" - in this species, a male who is a better parent has a better chance of passing on his genes.
- "Variability in male reproductive success" - in pair bonding species, most males have some offspring. In tournament species, usually one male per group (the alpha male) has offspring, while the other males rarely have any. You get more genetic diversity in pair bonding species that way.
- "Degree of sexual dimorphism" - in a tournament species, a male has to display his overall health and fitness to hope to be one of the few lucky ones who reproduce. This comes at a high biological cost, such as investing energy in growing huge antlers, or splendid plummage. Thus, while in a pair bonding species, the male has to expend resources on offspring care, in a tournament species, he has to expend them on metabolically expensive, and otherwise useless, secondary sexual characteristics - there is no option to just "save" them.
- Tournament species have high levels of male-on-male aggression, resulting in a lot of individuals being killed or maimed from competition within their own species. On a species level, this is kinda wasteful.
- From a species "point of view", offspring which is cared for by both the father and mother has higher survival rates than offspring which is being single parented.
Notice that these features are highly correlated - you don't generally get species where you get, say, low male on male aggression, but the fathers flunk on care for the offspring. So, to reap the benefits of being a pair bonding species, the dads have to invest significant resources in parental care.
Of course, the individual animal does not make such calculations for the good of the species - the behavior of the male animals happens because of a combination of physiological signals and social learning. It is highly unlikely that parental desertion will occur, and the few such accidents won't change the overall parenting strategy in the species.
To address the specific disadvantages you mention:
"Passes up a chance to mate" - he will be part of a pair bonding species, as explained above.
"Risks cuckoldry" - yes, he does. That's a known problem - in fact, one disadvantage of pair bonding species is female parental abandonement. Obviously, this is not sufficient to outweigh the advantages, since there are thriving species where dads do this kind of thing.
Transferring is dangerous - indeed it is, but I don't think it is that much more dangerous to move to dad's pouch than to mom's. See the discussion below though for "pouch exchange", which will probably impose a waiting period.
Sharing pregnancy seems to be a marginal advantage compared to the later raising - First, a marginal advantage is still an advantage, and animals take any survival chance they can get. Second, I doubt it is so small as you present it. It may happen for only a short time as compared to the later raising outside of the pouch, but it comes at a crucial time. First, the female's resources are most depleted right after birth, and having her come back to normal earlier can be the difference between life and death for her and the children. Second, oder orphans survive better! So ensuring best care and protection in the earliest weeks is much more important than ensuring it in the later years.
Also consider that even in the most typical tournament species, some parental investment is preferable:
even in a highly polygynous mammal, males may have to balance paternal effort with mating effort
Cheney, Dorothy L., et al. "The costs of parental and mating effort for male baboons." Behavioral ecology and sociobiology 69.2 (2015): 303-312.
All in all, the direction of your arguments is correct, but it is nowhere close to precluding the scenario from happening.
Is it feasible that the male parental investment is expressed as carrying half the litter in the pouch?
Possibly yes. I don't know of any species where this has evolved exactly this way, but there are several known cases of males incubating fetuses in some way. You have not only the penguins mentioned in the comments to the question, but also seahorses and frogs, as well as several other species.
Your choice of marsupials is already quite good:
In mammals, the occurence of biparental care is correlated with the production of poorly developed young while uniparental care tends to occur in species that produce well developed and large-sized young.
Lombardi J. (1998) Postpartum Care of Young. In: Comparative Vertebrate Reproduction. Springer, Boston, MA
Two features of your suggestion which are not seen in nature (as far as I know) are marsupials where the joey lives in the male pouch, and splitting the litter.
The biggest disadvantage to living in dad's pouch: young kangaroo joeys practically hang onto a nipple their first days in the pouch. Male lactation is theoretically possible, but it has never evolved, and there are probably reasons for it
Physiological barriers to the evolution of male lactation do not seem
individually insurmountable. However, the rarity of even partial or
pathological male lactation indicates that they are formidable. Although
experimental manipulations of both mature and immature males can
produce lactation, and although there is evidence of heritable variability in
the sensitivity of male mammary tissue to the induction of further
development, there is no indication that male lactation might ever occur
spontaneously in natural mammalian populations.
Daly, Martin. "Why don't male mammals lactate?." Journal of Theoretical Biology 78.3 (1979): 325-345.
But in the same paper, the question is asked
Is the reproductive capacity of a monogamous pair limited by the
female’s lactational capacity?
and the author hints that the answer is "no", so that would be a reason why male lactation never evolved. In fact, Lombardi mentions that "in biparental species, the female usually represents the limiting resource" - so if you introduce paternal offspring care as a strategy to increase a pair's reproductive capacity, because the female can replete her resources sooner (similarly to the penguin case), the question becomes why only offload half of the offspring on the father, when she could offload all of it. One argument I can think of is that, if one parent is caught and eaten, half its litter still survives, so it makes sense to not put all one's joeys in one pouch.
You might have a good argument for the separation if you set up an "exchange programm" as a kind of compromise. If the female carries all the babies in her pouch, her body is strongly taxed. If you give all babies to the dad and don't have him lactate, they starve. But if you have them exchange pouches twice per day, the mother only has to carry around half the weight, and does not risk all her children being eaten together with her, while they still nurse from her only, so you don't have to rewire the male's endocrine system for lactation. One problem here is the high risk of pouch exchanges - apparently birth is highly traumatic for marsupial joeys, since they are at a very early development stage and the movement into the pouch is very difficult for them, and some don't make it. I remember a moving description of it I read in some popular science book, either in Attenborough or Grzhimek, but don't have the original texts here to cite, but I found a nice illustrated explanation on the web, https://www.thedodo.com/why-kangaroos-have-pouches-1218814506.html. A look at the eighth picture is enough to see why it can't jump back and forth between pouches! So it would be more realistic to have the female carry them in the first days, but have them start changing into dad's pouch at some point, and that can be earlier than the typical "first journey out" for a kangaroo.
You should also consider that hardwiring teaching behavior for a more developed offspring in both sexes can be a bit "wasteful". For example, a mama leopard teaches her young to hunt, but a dad leopard doesn't. If your dad marsupial carries around half the babies, the time will come where they alternate between the pouch and the outside world, and start learning. It would be logical for the dad to teach a different set of behaviors than the mom does, which again argues for baby exchange.
Your argumentation would be somewhat tenuous, but I would say you can pull it off if you are careful.
If you need more information than provided in this already long answer, I would suggest reading Royle, Nick J., Per T. Smiseth, and Mathias Kölliker, eds. The evolution of parental care. Oxford University Press, 2012.