I like the "contract manufacturing" idea. With a grade in cost from --> Neutral or worse to --> loves you more than your mother.
I think that ship production should look like this:
1. Being able to take D-mod clunkers you've... acquired taken from red-shirts you converted into protein-flakes and turn them into pristine Hulls for your fleets to use. I think that any Colony should be able to do this, with a mechanic where the time / money it takes is directly related to the industrial power of the Colony (pop + Heavy Industry and so forth).
It should be easy as putting ships into a special Storage-like location for your Colony (i.e., just a new tab, not a whole new UI) called "Convert" or "Repair Yards" or something.
When ships exit the Repair Yards, they're automatically set up as a Variant and included in the player's defense fleets for this Colony.
This would fix a huge gripe with the current system, where I feel like capturing is largely irrelevant by midgame+.
2. Buy stuff from outside, direct (and in BULK, if you BUY TODAY WITH CASH). I.E., go talk to a Faction (preferably through the Comms interface for talking to Factions directly, which I presume is coming eventually) and offer to contract out for military or civilian ships. The Faction / location should bring up a UI of what they're willing to sell you (which you should be able to influence with bribes, good behavior and threats, if they're a vassal) and you should be able to "buy" the hulls right then, but actual delivery will take a while.
3. If you've got Heavy Industry up, it should be possible to directly inject cold, hard cash into that process to speed things up. "I don't CARE what it costs! I want that Cruiser YESTERDAY!" should definitely be a thing. It should cost ridiculously-exponential amounts (say, 5X base purchase price) to make your local Shipbuilders Union drop everything else on their plate and get the work done fast, though.
4. You should be able to adjust local tax / tariff rates to Make Stuff Happen faster, when you need to. I like that the Economy doesn't feature much Guns and Butter nonsense, but that's something that's potentially Fun; adjust your War Economy to either pour in cash (that you'll spend tactically at a crucial Colony you need defended) or lower taxes to very low to encourage industrial output.
5. You should be able to make weapons via a Light Industry upgrade or by pouring cash in (just ask Mattel about making M16's or the countless other weird situations where American consumer-goods firms have suddenly become military-goods purveyors).
6.