I would do 3 coats, quick block with 400, just to knock the surface peel, even if a few shiney spots are showing here and there, then REALLY block it down with 600, then re-clear, sand with 1500/2000 if everything goes right and buff.
After doing this one I feel that would be the next step, and in some ways, may even save some time.
My booth is nothing special, that is for sure so I understand when you say you hate to sand twice, but I think it may be easier in some ways as well. It takes a lot of sanding to sand the coarse scratches out, then when you miss some you have to re-sand and buff those spots, with the 600 you can get it flat a lot faster and I think you could even make it flatter if you could sand more with the 600 and less with the 800-1500.
the key is to lay out that second session of clear so you don't have to sand that so aggressively.