Here is a link for buckram, Sorry I spelled it wrong before
http://www.hatsupply.com/foundationfabric.htm
Also, a suggestion for using interfacing if you want a flat ornament would be to use fusible interfacing, it is really easy to work with. Use it on both sides (front and back). If you wanted to hand sew them together with a decorative stitch you could then, as long as you had a sharp enough needle, not ballpoint. You wouldn't need to turn them then, although I question the idea that turning them would remove the stiffness.
If you machine stitch them and have used the fusible interfacing, you would want to stitch first, then iron the interfacing just inside the stitch line so you don't end up having the extra bulk of turned interfacing.
Oh - or if you use non-fusible interfacing, you could do a sandwich with a decorative machine top-stitch (zig zag?) to hold it together without turning. This would eliminate the bulk of the turned interfacing.
I also did want to mention that I have many starched crocheted ornaments and have never had a problem with little critters. That said - instead of starch, you could try stiffening with glue (like the white elmer's school glue) or wax. If you do either of those, you would likely not need any internal stiffener. I'm really liking that solution as I think about it. I'd probably do the wax if I was to make these, but the glue would be cheaper and easier.