If you want to try it on the less expensive side of things, get some of those anti-fatigue EVA floor mats that cosplayers use. They're about 3/8 to 1/2 of an inch thick and usually have a texture on one side, but since you're going to bury it inside a puppet, it shouldn't matter. A lot of stores have them now, I think Harbor Freight had some on sale the other day I was in there. 4 piece squares 25" x 25" x 1/2" for like $8.00.
Here's a link to a good description of L200/EVA: http://punishedprops.com/2015/02/23/l200-foam/
Good idea. Harbor Freight is just up the street from me too.
No go on the Harbor Freight foam. Seems to be treated and after layering too heavy for puppet. Not sure if I got the right sort of thing. Looking at alternatives. . . stay tuned.