I have no confirmation, but I suspect that the -A on the Enterprise was another cost saving measure, because it would be easier to add more paint to the original model than paint an entirely new registry.
They may as well have, the alignment is different because "NCC-1701-A" is wider than "NCC-1701." All the registry numbers on the model would've been entirely removed and reapplied (you can see it clearly in the intro shot; in the first three movies, the registry on the top of the saucer was centered on the "-", but on the A, it's centered on the first "1"). Plus, they would've already had to do more work than reapplying the numbers removing all the battle damage from TSFS.