I'm getting ready to start a combination "stack the deck" / crazy quilt using QAYG but want to embroider on it. Do you think I should do the embroidery first with stabilizer or just do it right through the batting. It will look kind of weird on the back I think. I'm thinking of doing some denser designs, not just a quilt patter or fancy stitches. Any thoughts?

So like a full butterfly embroidery motif?
I would do those before the quilting. So just fabric and stabilizer.
I think it would work technically, but wouldn't look so great on the back.

However, if it's just one of the fancy stitches - like the hearts or vine, then you can do that with the batting/backing.
And that will look very cool on the back (if you use nice thread in the bobbin, that is).

I'm thinking of doing a variety of things -- butterflies, flowers, and who knows what else. I have over a thousand designs just screaming to be used. It's time! Stabilizer it is!

I used a great butterfly embroidery on many blocks before making the quilt blocks. It turned out beautifully. It would be next to impossible to hoop a sandwiched piece---too thick.

I would do just stablizer then you could stitch around the item you want to pop out once the batting and backing are on.

Definitely. The border on mine was a row of butterflies along the edge. It really did turn out better than I had expected.