I'm not a diff expert, but if my diff was whining, my first thought would be to rebuild it. Diffs aren't really known for wearing out, but if it is, my second thought would be to just go get another. Yours is likely a 3.54 which should be easy to find for a reasonable price.
As for the problem with viscous diffs, my understanding is that if used hard, as they would be on a track, they get hot, and just kinda stop working. And I could be wrong, but at that point I think you just have to replace the diff. I would only ever consider a CLSD or helical/torsen.
The MFactory helical LSD mentioned above would likely be a good choice. There is also the OS Giken Superlock is another option which is a clutch LSD, but also quite a bit more expensive. I know Quaife LSDs used to be available, looks like they still sell them for R200s, but not sure if they're for short nose or long nose. AFAIK you can put a long nose LSD into a short nose with some work.
There is also the Subaru option. Pretty easy swap, should hold up fine if you're only going with stock VQ power, especially if you won't be launching or racing the car. They came in both CLSD and torsen, a 3.54 torsen should be pretty easy to find. This may actually be the easiest option of all.