Sounds like a good idea! Would it be too much to make a separate mode (like the option with whether you'd like to play the story or play the incremental mode) where you can construct new or additional ships via the shipyard (like in the previous games)?
You could possibly gate the ship designs behind unlocking them normally, where it rewards you with the possibility to build it instead of giving you the ship immediately.
A means to balance this ingame could just be to leave the stat multiplier upgrade path out from the shipyard (from the previous games) and replacing it with something like building speed or a way to store ships from your team?
(on a more helpful note; like in HX1, the inventory slots fit outside the window at more than 90 slots. Is it possible to hardcap that like ship dodge/ship crit rate?)