There are at least two designated spots on the Isolation trail, and I think 2 more on the Davis Path heading towards Washington. They are not on the maps, but they are easy to find and they certainly won't be full on a Thursday night. Water is close by the Isolation trail, the ones on Davis may require you to hike back down a short ways for water.
Once there, Isolation is just a short jaunt. You can easily do it before dinner. Keep your eyes out for summit spur trail sign, it's sometimes hard to spot.
Parts of the Rocky Branch trail get very muddy after rain, and it's nasty mud. Don't pack too lightly for your summit trip, you'll be exposed the entire time. You can fill up water at Lakes and the summit so you don't need to carry too much to start. I wouldn't even break down your camp, leave it set up and come back to it after your summit day. That's what base camps are all about.
You could head out via the Glen Boulder trail, but then you'll have to do a short road walk to get back to your car, or follow the Avalanche Brook ski trail back. Keep a close eye on the weather, don't be afraid to turn around. Don't keep going because you can use the summit buildings. You'll have to come back down and the weather is just going to get worse as time goes on, and you'll be more tired and there will be less light.
Here's a
trip report that covers a lot of the trails you'll be on.
-dave-