After playing a ridiculous amount of time, I finally figured out a little trick that vastly increases my power in every game.
There comes a time in most midgames where you want to mass-produce fully loaded starbases. That requires huge numbers of constructor ships. But by that time the default constructor ship is up to Mark 5 or even much higher, so they're very expensive to build.
You need a few high-end constructors for things like seizing distant precursor relics.
But for starship build-out, you need to design a Cheap Builder. That's a small hull + a constructor module + plus two of the cheapest engines. Most shipyards can crank those out in 1, 2, or 3 turns. So you can spam like crazy.
This game really has an awful lot of depth. I'm sheepish it took me so long to figure that out.