Marshall, just my two cents:
Before worrying about transports there are a lot of much more critical enhancements to be answered to improve the
game, like - to cite a few - loaning units WITH leaders, loaning ships, awarding political points (pp) for loaned
units involved into battles, halving the pp gained/lost in naval battles, giving Constantinople control
over the Dardanelles, reintroducing the Kingdom of Italy, allowing single defending corps to ask for
reinforcement from nearby troops (now AI runs them and does not), fix corps landing from blockaded boxes.
These are all extensively tested EIA features and their lack significantly unbalance present gameplay.
About transport movement allowance and game balance.
Original EIA had some optional rule to limit fleet movements in large stacks and/or transporting troops.
Anyhow this limit could not reduce movement below 4, so increasing transport movement to 4 could be reasonable.
On the other hand, it could be a very good idea to to reduce the movement allowance of heavy and light fleets transporting corps to 5 or 6.
On reverse, higher movement rates for transport or other strangeness could seriously unbalance the game.
(...) the possibility [for transports] of acting as an automatic depot for troops actually in that sea zone would be useful. In other words, don't require the troops to land if there are transports present, and don't make the transports have to have a depot to supply them (...)
is absolutely foolish.
Presently, the only way to transport troops over long sea distance is to have some intermediate place where to land them. This gives great strategic importance (as it was historically) to places like Malta, Corfu, Gibraltar...
Spoil Malta and Gibraltar from GB and you would have cut its access to Mediterranean. Change the rules as Jimmer suggested and GB will not care at all about those strategic possessions. Let corps stay at sea for more then one phase, and you will see huge armies waiting months at sea the right moment to land on enemy soil.
More generally, the smallest is the "sea range" over which you can transport troops, the more important are strategic considerations. The longer gets the sea range, the more minors importance is solely determined by their money/manpower contribution.
If Turkey wants to project in the entire Mediterranean, for instance, it has probably to conquer either Sicily or Tunisia. Spain and GB, knowing that, will oppose this policy. Spain too needs the south of Italy to project east. Give Turkey the ability to project everywhere and it will invariably open his game in Jen 1805 by declaring war to Egypt, Tunisia and Algeria at once. Maybe to Tripolitania too.
Moreover, even if GB has a huge fleet, it will keep it invariably busy blockading French ships and guarding the channel from a Spanish betrayal. So you are left with your transport fleets and your Malta and Gibraltar bases to bully around on the African coast...
Finally, remember that this is Napoleonic era and not WWII. Amphib operations were extremely difficult to realize, and I strongly suspect that even present rule make them too easy to plan/realize.
In conclusion, my advice: do not increase transports movements above 4, DO NOT let corps stay at sea for more then one month and seriously consider reducing other fleets movement with corps onboard to 5 or 6 (maybe 6 if <= 5 factors onboard and 5 if more then that).