Update:
I took the case off and loosened the screws nearest to the spacebar, which allowed more play between the barrel plate and the other layers. I was able to move the hammer around this way, but it did not settle in place, and was now obviously out of place.
So, I fully disassembled it, reseated the hammer (it looked fine but I swapped it with the Pause hammer just in case). Replaced a few screws, then plugged in to test before doing them all.
No change. When plugged in, space kept repeating. AND, the spring and hammer still seemed really stiff compared to all the others on the board, as if still somehow pinched.
I loosened the screw nearest the spacebar a little, which made it stop repeating, but now it required bottoming out completely to register. Tightened a little, and then it was working right. Seemed really finicky especially considering all other keys worked fine.
Reassembled fully. Plugged in. ..and now, nothing!
If I take the board out of the case and squeeze the barrel plate against the metal right next to the space bar barrel, it registers key presses from that action alone. But pressing the key does nothing.
I'm not sure what to make of this.
The parts appear to check out, but for some reason the hammer in the space bar position doesn't move as freely as all the others and even when I sort of got the switch working, it was abnormally sensitive to the tightness of the nearest screw.
So...something is not right. Maybe that barrel is slightly warped and is affecting hammers installed in the spacebar position, or maybe there's something wrong with one of the membrane sheets? I'm not sure, but it's not obvious.
Also, now I don't even think that hammer WAS out of place to begin with, since it's behaving the same way physically, when it is seated correctly. (The spring sticks straight out, and does not flop back and forth like the others when the board is tipped away/toward you.) If this is all stemming from a hammer problem, it's due to something less obvious than an out-of-place hammer.