Got around to looking at the save (thanks for uploading it!)
Seems the fleets are so big mainly because of the Star Fortress with alpha core. It's generating 189 FP of combat ships (before doctrine modifiers) to match the patrols from a size 4 High Command... and 870 for the station. Also, it turns out that contrary to my previous belief, alpha cored HT Star Fortress does not actually kill infinite ships.
I'm reducing the strength estimate multiplier for stations in the next version, by about 30%.
I then had people tell me that it arbitrarily limiting the ships I can deploy when the enemy fleet was under no such restriction was it working as intended.
Enemy obeys the fleet cap in the same way that player does.
You can increase the limit in settings as Axle suggests, if your CPU can handle it.
Would it be possible to order the construction of a fleet to follow you for <X> days, in a similar way of putting in orders for base strikes and invasions?
Most thinking it'd be nice to order a custom sized fleet to have the set orders of following you around for a time (say, 60 days, or something that you assign with a slider?) if you want to go crack some REDACTED heads on the fringes of the galaxy.
I could do something like that somewhere along the way, yeah. (I'd need to find a way to get the AI to follow the player reliably though, the Follow Me implementation is a bit of a mess)