How big is the stretch? If he's big, I'd stick to your idea of switching based on matchups, but if he isn't that tall, then maybe a GC Center is the way to go.
I also wouldn't rule out a big LDD, especially since you have no real defenders on the team and stretches stink for defense.
Personally, I don't like the stretch big archetype and would rather have a big with 60 3pt shooting, so he can still stretch the floor, but also be a proper big.
You have a lot of offense, but not a lot of defense going on with that lineup. Good idea on the Glass Cleaner - I think it will help you guys whether PF or C.