I'm using Edelbrock's thin little zinc adapter plate (like an 3/16 of an inch or something) to mate my AVS up with my spread-bore Performer manifold. It doesn't seem to be sealing too well - the idle hangs for a half second when I rev the engine.

The adapter plate included a square bore gasket only - I have that gasket, the plate, another thin gasket and my carb. My carb rebuild kit also came with a big thick rubbery gasket about 1/4 inch thick that I haven't tried out.

Am I supposed to use this plate with a spread-bore gasket between the plate and the manifold? Is it supposed to go metal-to-metal? Or should I just forget all of this junk and use the big thick gasket?

Use the thick gasket!

You need a thin square bore gasket between the spacer and the intake , ore use some type of hardening sealer that is not affected by the crap we get for fuel.