Addressing the issue of unit size, individual pieces in Axis & Allies typically depict the Corps or Army level, as I understand it. However, there are a few deviations to depict smaller, independent commands, such as the two British infantry in Hong Kong and the French and British infantry scattered in West Africa south of the Sahara.
I understand the desire to be able to build every type of unit, but I think that scarcity places correct emphasis on those troops’ elite status. The mobilization rule would be a quirk: the Legion has periodically fought on the mainland (as during WWI, for example). Its frequent foreign deployments are rather a reflection of the fact that the Legion’s peculiar non-national composition gives French politicians greater latitude to pursue foreign policy that has some blood cost.
I think that Frogmen should get to roll a d6 against every capital ship, hitting on a 2 or less. They should have no independent combat value because they operated as small units, not at the division level.
When it comes to Marine infantry, the question is whether you view naval units of any type as indicative of fleets (e.g., a Destroyer could stand in for a single capital ship), or whether you want them to represent actual unit types, in which case I don’t think a Cruiser or Battleship should be allowed to carry Marines. Historically speaking, Cruiser divisions sometimes fielded Marine and naval landing parties, but these comprised perhaps slightly over 100 men when multiple ships combined their detachments.
Think about whether you want to confer advantage to certain units only for certain rounds of combat. The difficulty of remembering when and how to roll for them can be partially mitigated by player aids.
One additional unit type for which HBG makes a piece is the Armored Car. This is especially good if you want to game out the inter-war period. I have developed rules allowing attackers to re-roll a die when an Armored Car is present in the attacking force. This is a play on their role as reconnaissance elements. Think about Cavalry, also. Perhaps Cavalry strike harder versus infantry when they outnumber defenders.
I’ve used cards to trigger the appearance of special units denoted by markers. They can also be used to grant nation-specific bonuses for a single round of play, etc. This works better on much larger maps with a game that is expected to go on a while, especially because the cards can be used as interrupts, which prevents players getting bored between turns.