This is only a suggestion, but instead of reinforcements, why not issue repair points after each game?
Each player will get 1 'Battle' point of repair after each game - regardless of winning or losing. Winners of course will get more points.
That way, after each game the player can either get back a single Battle class ship, 2 Raid, etc. but only from his fleet listing.
So in the final game, he will have at least one battle point on the field, plus anything he has left over.
As a caveat, I would add that you only get repair points if your ships are damaged, just in case someone plays and takes no damage at all.
Also, the player could mix and match the points such that he can use them to repair ships he still has up to full strength or pick fresh ones.
Example - During the first game a player loses a Primus and a Sulust, but has left 2 badly damaged Demos.
If he repairs both the Demos up to full strength - Then he only has one Raid point left from his Battle point repairs, so he can't bring back the Primus, but he can now bring back the Sulust.
Only a suggestion guys!