It turned out alright! It's a little fluffier, stretchier, and a bit too sticky but the kids really seem to be enjoying it, and I love that it is completely safe for them. I guess I'll have to keep perfecting it, but for now it works for us. :)

Here's the recipe:
1 cup Bob's Red Mill All Purpose Baking Flour (this is GF)
1 cup water
1/2 cup salt
1 tablespoon canola oil
2 teaspoons cream of tartar
1/4 teaspoon Xantham Gum
Put all the ingredients in a pan. Stir constantly until it forms a ball, using low to med heat. We used a little cinnamon for interest, and added a bit more oil afterward to help with the stickiness.
That's it!
Update: This recipe was a flop! After it had been refridgerated for a day or so, it was too tough to play with. It was more like therapy putty than playdough. I'll have to try again another time!
Update: This recipe was a flop! After it had been refridgerated for a day or so, it was too tough to play with. It was more like therapy putty than playdough. I'll have to try again another time!