The Dana 44 rear diffs in our trucks usually last forever w/out any issues. You should have the limited slip rear w/ your '99 LS. The only touchy issue with them is to make sure you use a tube of friction modifier for the limited slip clutch packs, or you will get some chatter, not humming though!?!
. I'd have a good driveline shop check it out & see what they think.
G/luck
Joel