I've been lucky enough to stay at White Crack a couple of times and it's good. It's amazing for stargazing. I prefer Murphy to be honest but White Crack certainly is vast. Bring a 'scope or binoculars.
This was early March of 2020, which was a relatively dry year. Mud and snow weren't so bad and I was able to get in from the Shafer side without issues.
Jeff, Ann and I got it August of 2019. This was brutal during the day but tolerable at night.
BTW, if you do WRT in the summer the pick spot is undoubtedly Hardscrabble. Not so much that the camp itself, it's exposed and amongst the tamarisk. But it is right on the Green River and you can spend the whole afternoon soaking in it.
But I think Taylor is a better camp for isolation. It's further off WRT so there's a bit less day traffic. The people coming in are due to it being a trail head. This was early November and the weather was perfect.
Taylor's also close to the end so it's not an obvious choice in an overnight itinerary, which works in favor sometimes. I had it two nights and saw one other hiker in Tundra and a couple in an Volvo 303 the whole time.