While I will happily agree that the combat system could use some modification, I have never seen a "one of mine goes, then one of yours goes" system that doesn't a) bog down and b) end up with its' own problems - like the barrage of units at the end of the turn when one side outnumbers the other significantly.
An initiative system based on indivdiual ships (when not in fleets) and fleets would be interesting. A random seed would be set for each individual ship, and one for each fleet. Each ship which is not in a fleet could be a "manuever element" and each fleet would be one.
Each ship or fleet would add it's experience rating to the seed, and maybe if there were race traits for initiative, those could be added/subtracted as well. Then, in order, each element performs an action set.
This would combine the "balance" of "one of yours/one of mine", but would tip that balance in favor of the units with better initiative. So it may be that two or three of yours go, then one or two of mine, based on the initiative scores each turn. I would keep fleet initiative as well, but enforce that only the fleet leader can be selected for movement, and the other members hold formation. That gives the fleet a huge firepower advantage when it activates, but removes the temptation/allowance for each ship in the fleet to move individually and separately. One of the cheats (IMHO) that used in tactical against the AI was to move my fleet members where I wanted them, typically burning all of their movement, THEN move the fleet leader so that they don't stay in a formation that I don't like (this was way back when there were fewer formations available).
This gives an incentive to operate in fleets, but allows flexibility if you don't. And gives individual ships more tactical freedom.
Just another opinion, and worth what you paid for it.
General John