I camped at Trail Camp one week ago. At the time there was ample space off the snow to camp. Given the warm temperatures and rapid snow melt there is probably even more space now.
One thing to note about Trail Camp. The marmots are a real pain. These things are really smart and resourceful, and they tend to come out a few hours after sunrise, usually when the camp has been nearly vacated by those heading to the summit. They will steal anything they possibly can. If you leave your packs and gear outside your tent, assume they will be moved, chewed through, or stolen. I didn't end up going to the summit because I was feeling some ill effects of altitude sickness, and I spent the entire morning fending these things off. My suggestion is to put all your food in a bear canister and leave it away from your tent. I also say you should put all your packs and equipment inside your tent and seal it. I have read they will chew through your tent, but I didn't observe any of that at camp.
Good luck to all!