Incompatible front derailleur/crankset?
First of all, IMHO, when you buy an old bike you should always change inner and outer cables (cable housing) for the brakes and shifters. This will ensure that the cables have low friction and won't get stuck somewhere

Then this part "It's ~8mm from lowest to 2nd and ~5mm from 2nd to highest" makes me think that someone got the order wrong. I think the highest and the middle sprocket are on the wrong side or the crank(outer side). Or the smallest sprocket has spacers that shouldn't be there. Or maybe the middle one is lacking spacers.

99/100 Sprockets are equally spaced, because that's the way the shifter handle pulls.

Lastly, check the "front" dereaullier alingment. It should be parallel to the sprockets.