Doing some more work on my Gibson LP Studio. Needing advice from guitar techs/knowledgeable guitarists.?

It's a good idea to replace the nut because Gibson's Corian nuts are sh*t. If you're going to use a sort of metal nut, go with br. A br nut makes more shimmering highs and makes the guitar more harmonically responsive for a lot of reasons I won't go into. If you can afford an ivory one (I think you mean ivoroid), go with that or bone, or Tusq if you have a bit less money. Gibson Les Paul Studios and SGs are notorious for not holding tune (not widely renowned, I mean among those of us who know a thing or two) and there are a lot of ways to fix it, but I don't think the Tune-O-Matic bridge is an issue - it's a myriad of other problems and your Bigsby on a guitar that isn't meant to have it. Better quality tuning machines will not prevent your problems, but they can help. Bring it in to a good luthier who can fiddle for a while and find out specifically what's wrong with it.