The quilt doesn't have to be soaking wet to block. Steam would work, and so would spraying it with water - I have a spray bottle I use just for this. I've never had a problem with fabrics bleeding after I sprayed.
I haven't used foam core, but I did buy some interlocking foam tiles to put on the floor under the quilt. It's easy to get the pins in, and softer on the knees.
Janet