I do a lot of this. I gave up on paper separators for glue blocks on
large bowls (anything bigger than 8") years ago, they fail, even if the
wood is dry.

no squeeze out sounds like it's not flat. Check with the block dry and
look for light through the crack before you glue. Use a hand plane to
make them flat, or match curvature. Sometimes even not flat can match
well if you rotate the block.

Don't use Gorilla glue for this application. I've had a few large
pieces fail with the gorilla glue. previous post about foam is right
on. Titebond is the best, but wait several days, even a week if you're
concerned about the moist wood.

Epoxy works well. Super glue can work, but super glue has to be done
quickly and there may not be time to clamp before it crystallizes, I
wouldn't use it for a large bowl.