My car makes more of a grinding noise under load rather than a whine. I'm sure it's the pinion bearings. I replaced fluid. Still did it. Pulled both rear axles, had them checked for straightness (and they were), put new axle bearings and seals in. Still did it. I've been driving it like that for 3 years. I even took the car to Marion last summer and ran it 10 times in one night. Granted, I have street tires, so it didn't hook for shit.
Irregardless, instead of dropping more cash on my rear (the car, not mine), I'm saving for a 9". But that's because I want to hit some track events. If I knew for sure that I wasn't going to race it anytime soon, then I'd just have the 10 bolt rebuilt.