Congrat's on getting a new living room! I do hope you are able to bring your bunnies back inside.
We are having terribly hot weather here in Mich, in the 90's, and it's very hard on the buns. You might put a pop bottle of frozen water on it's side in the cage with them so they can cuddle up to it and cool off. Please be sure that they are protected from the sun too. Good move to get the wood on their cage floor.

And don't worry about buns lounging/sleeping in their litter box. It IS perfectly normal for all rabbits to do that. I think it's because the box has sides and they feel safe in it. SOOO...the trick is to keep the litter box cleaned out and not let it get skunky...they're not THAT discriminating and they'll get skunky too if you don't. Good luck!