Well okay, I don't give up easily. I wasn't happy with my first try (the post below), so I tried again. I like these better. And once I pretty much accepted that I wouldn't get much, if any, dimensional texture with the brand of gesso I used, I was reluctantly okay with that. On these I sponged the gesso onto the stamps, and stamped onto the surface. Which I had also gessoed, and let dry, before I stamped. I think one reason my first piece, Doodle Bird Haunting, seemed so washed out was because I stamped onto the brown side of the pizza cardboard, then painted over it. It didn't allow for much contrast with the paints, I think. I'm glad I learned from that.
I did use straight caulk sponged onto stamps, then stamped onto another piece. That gave me the dimensional texture I wanted and expected. I love that stuff!!! However, it didn't show up well at all in the scan. But I like that piece, and will most likely use it for the postcard swap.
So, I guess all is well that ends well, and I learned some things along the way about gesso. Thanks for all the info about gesso people gave me, in comments, and also in yahoo groups.