Phil, first off, you are probably not allowing enough time to visit both Deep Creek Hot Springs and prepare for Mt. Whitney. It's about a 4 hour drive from Deep Creek to Whitney. And you need to start hiking Whitney EARLY on that Monday if you get the lottery. So that means you should be at a hotel in Lone Pine or camping at Whitney Portal Sunday night. So you really wouldn't have enough time to hike to and from Deep Creek and enjoy any time at the springs. If you can, I'd suggest going to Deep Creek on Saturday instead and enjoying a full relaxing day there, then drive north on Sunday.
As a regular, yes weekends suck for me because of more crowded conditions and less nude people. But if you absolutely have to go on a weekend, and if you think you'll never go again, then by all means go. Even though there may be more swimsuits than nudes, the vibe is usually relaxed enough that no one will hassle you nor should you feel awkward if only you or just a few people are nude.