Sounds similar to the rules I ran under for one show in 2006. I had recently been given a 377 with double hump heads. All Standard stuff, GM Crank, 2 Bolt 400, Worked over Humps and a shelf cam. It ran pretty well. I'd say your heads will be Ok, as this motor was an A-Mod motor that we put a 2 barrel on. You'll want to be sure as you said to have the camshaft fit to the heads and intake along with carburetor and car.
I sure miss when you could run with a $1500 cheap motor!!