My preference would be for no purchase limit, since that seems to me rather unprecedented for A&A, at least since the earliest rulesets of Classic.
The USMC may have had 6 divisions in the war, but I’d rather preserve these units as a generic “Elite” type, and not pigeon hole them into a specific description as marines etc. I think trying to create exact ratios for a unit sculpt to historical division numbers is always problematic. Better I think to leave the purchasing as normal, without limits, and leave it up to the players discretion to decide how many to buy.
If the 5 ipc cost is the sweet spot rather than 4, then perhaps just increase the functionality/ability of the unit so they can also serve as airborne? Another combat role beyond just the amphibious invasion. I think this would be the ideal solution, since it gives the US for example, a way to have these units used in Europe without breaking with whole Marines only in the Pac thing.
Perhaps these units could have their abilities associated with units at bases rather than just with units. For example, Elite ‘marines’ can only embark on the battleship if it moves from an opperational naval base. Or similarly Elite ‘paratroopers’ can only hitch a ride on a bomber if it takes off from an airbase. Or something along those lines. This seems a bit easier to me than introducing a separate class of infantry for each nations potential elite infantry. Just make it into a catch all.
Basically I’d put the focus on the potential strategic movement advantage, rather than the attack/defense value for the cost. Even if they had the same value as a normal infantry unit in combat, the ability to move in ways that normal infantry can’t would be a pretty strong incentive to buy some, without unleashing a spam that might occur if the unit is significantly stronger than the inf artillery combo. We don’t want the elites to totally eclipse infantry as the go to ground purchase, especially for nations that have to move across the sea to reach the action.
Using bases to cap the number of Elite units that can be used at a time seems more convenient to me than using the associated units. For example, instead of a bomber or Battleship spam resulting in a cascade of airborne and marine attacks, you could cap it 1 Elite per base per turn.
An Elite at an NB is considered a Marine, an Elite at an AB is considered airborne.
This would encourage the building of naval bases in the Pacific to move Marines around on battleships. And if used as a paratrooper, tying the elites to the AirBase rather than the bomber would place some limits on their use, like Germany in the dark skies for example.