Will my 8-3/4 hold up behind a 4 speed?

hi, the 8 3/4 will live very well for what you have. there are things to consider with this rear end. the clutch pressure and disc will have a say on the life of gears. as long as you can spin the tires, should be no problems.
how ever, slicks and dead hooking will shorten gear life. as will lifting on the shifting. otherwise, it's strong enough. btw, get a 7290 or dana spider makes
a 1350 yoke for 8 3/4 rear end. I have a 1350 in rear and 7290 in front, both have held up very well.