Bottom Bracket still feels dry/tight/rough after two overhauls
 

First, I've done multiple successful BB overhauls in the past (though I could still be doing something wrong). Also, I'm reusing the caged bearings, if that makes an difference.
I recently bought a bike, and the the BB was really rough and dry. No problem, I greased it up and reassembled everything. Went out to ride it, and it felt a little better, but definitely not smooth. Tore it down again, packed a bunch of grease in, and it still feels rough. Should I replace the bearings? Also, it seems like the grease is getting squeezed out of the races, but if the BB was any looser, the cranks would be knocking around.

Did you remove all the grease and inspect the cups, cones, and balls for wear and damage?

The balls (bearings) are rarely, if ever, implicated in bearing feel. What would matter is the condition of the races -- spindle and cups -- specifically the ball track on those.

If all looked OK, my first guess is that you installed the cages upside down (inside out). Take it apart and flip the cages over and try again. I say this even if you're 100% sure they're right, because I've seen so many cases where folks were 100% sure, but wrong.

If you don't want to take it on faith, here's the way to know for sure (correctly). Remove the spindle and one cup, clean thoroughly, and assemble the spindle caged balls and cup dry in your hands. Observe and feel if the cage is touching anything, flip over and observe again.

BTW there are a few types of retainer cages and all share the problem of keeping the rib out of the way. Among metal cages, the rib can be of a large diameter and ride outside of the spindle, or of a small diameter and ride near the center of the cups. The diameter of the cage compared the the spindle bearing lip and shaft diameter is a good predictor of where it goes.

Now I feel stupid. I inspected them on the first overhaul, but, sure enough, the fixed cup is pitted. Thanks for the help!

It's easy to miss. The cups are usually not the first to go.

But if the cups were good, (a) yes replace the bearings, as they're only a dollar or two for a BB worth, and (b) a great way to avoid the cage in/out question is to just not use cages. SB recommends loose balls. Loose Balls, not just for fertility anymore...