where to start on this one???
well on a 99 Z28 (my year too) the posi should be a zexel torsen helical gear type, if you want to read about that. You wheels will spin oposite ways like open diff when both off the ground if it has. There are no wearing parts as it were on these so nothing to worry about with regards to any kind of planet gear as they dont have them (or clutches like the auburn type) also you DONT need any limited slip additive in these to make them function but it makes then quieter.
With reagards to the whine, is it loud/quiet, and deceleration or accel or constant speed. As far as im aware its due to a 'bit incorrect' lash setup so the gears dont mesh perfectly. You'd have to pull the diff cover and check the lash to see if it is within recomended specs. I did here that on post 2000 cars many diffs were put in a bit tight so made noise.
I DID worry about this at the start when i got my camaro but now aint too bothered, i swaped out the 'noisy' diff and put in an auburn clutch type more an LSD rather than a posi, this failed after a year of drag racing and 'crappy' oil and was on the verge of detonation when I took it out (the springs were really loose and were hitting the planet gears). Anyway, got another zexel axle from a TA WS6 and put that in, and it was off a 30K car and still makes some noise, but i'm not too worried. it drives fine and when i get it on ramps the noise dissapears and only happens when drving, sod law.
Sorry for mammoth reply but really upto you if you want to leave or sort out. Also a axle on ebay for about 300 if you want another
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'99 Z28 A4, 253 LS2 heads, 228R TSP cam, Patriol Dual Springs, Double roller timing chain, LS6 ported oil pump, OBX LTs, 3" True Duals, LS6 intake, 42lb/hr injectors, SLP lid + bellow, EFIlive COS 3 Speed Denisty Tune (self tuned), 3200 Circle D stall, CAI mod, KYB AGXs, Eibach Pro Front Springs, UMI panhard, LCA + Brackets, Strut Brace, Custom Subframe connectors, WS6 axle with 3.42s, 18" American Racing Rebels, US mirrors, 93 tail lights, 3.5 inch custom cowl hood. Mickey T's Street DRs on Vette-ZR1 wheels for the strip !
Best ET: 12.0 @ 116 mph (on a 0-60ft of 1.8 s)