Presidential Traverse - camping recs for 2 nights

A few friends and I will (hopefully) be completing the Presidential Traverse in the White Mountains in July. I'm keeping tabs on the closures/openings of trails/areas and so far it seems July 1 is the re-opening date for spots along the route. We won't be using the huts (those are closed because of COVID) so we'll be camping. Two of us will have hammocks and the other two will be using a tent. We have to go below tree line, so I was wondering if anyone had any recommendations for routes/locations along the traverse to plan out and set up camp. I'm well aware that going below tree line is a significant detour, but were here to enjoy the great outdoors!

Our itinerary is 3 days, 2 nights. The first night will probably camp near Mt. Madison.

Any recommendations are helpful!