Even though I'm angry at Biotene, I tried the Gentle Mint version of their toothpaste. It is actually burns less than any of the others I tried.

I also found that GC (the makers of MI Paste) have an oral gel called GC Dry Mouth Gel. I tried it. It's very gentle. The flavor level is very mild. It doesn't seem to have as many helpful ingredients as Bioxtra, though. Diglycerol, water, gum carrageenan, sodium citrate, flavor, and ethylparapen.