I think these are all great thoughts, peregrine23. I'm not sure how carriers will fit into the current scheme (in terms of the number of additional ships in battle), but even with carriers, I'm not sure the max number of ships in battle will be very high.
I think more logistics would be good, but maybe there are other (additional) ways to increase fleet size (one of which is already in game but doesn't seem to be functioning).
1a) The Hyperion Logistics improvement is intended to reduce the logistics of ships being produced at a shipyard. It doesn't seem to be working, at present, and so once this is functioning, fleet sizes could be slightly larger.
1b) I don't believe the Hyperion Logistics improvement is presently affected by bonus tiles. If it were, then well-placed logistics improvements could have a major impact (making a huge hull cost only 7 logistics, for example).
1c) I don't believe the current Hyperion Logistics improvement effect is intended to stack if multiple planets sponsoring a shipyard have this improvement. Perhaps the effects could be cumulative.
1d) Or, instead of removing a logistics point from a ship, the Hyperion Logistics improvement could add to your total max logistics points, but not as in GCII--make it so each planet can have one, and each improvement's bonus is cumulative. So each logistics improvement that is built would increase total logistics. If these were expensive, this would help prevent too many being built too quickly and would be a good late-game method of increasing fleet size to gain a tactical edge against high-power opponents.
2) More logistics techs could be added to increase the maximum (perhaps in different tech categories).
3) Logistics could be calculated slightly differently--instead of calculating each ship individually, smaller sizes (tiny and small) could be calculated in squadrons. For example, instead of each tiny ship counting as 2 logistics, make it so something like 1 to 5 tiny ships cost 2 logistics and 1 to 3 small ships costs 3 logistics.