If every horse could run in a snaffle, you'd see a lot more NFR qualifiers trying to run them. You could try switching up to a twisted wire snaffle, the twisteds are harsher but not really "Oh-my-god-abuse" worthy by any means, unless you get them wire thin. You can pick one up for $16 at Big R [It says "Are" because of the filter >.>] in White City or the Horse Blanket would have them I'm sure. They had them full cheek and loose ring last time I looked, and I run Bailey in a full cheek.
Billy Allen's are a little bit on the expensive side, but some of them aren't too bad. Billy Allen Bits
Also, I was thinking back to what my other barrel horses used to run in. If you don't like the billy allen, you could try a Simplicity bit or a "Delight Smooth" by Carol Goosetree. I've never had to try a Loomis on my own horses, but I know several people who have ridding in the Loomis draw gag.
Here's Dena Kirkpatrick on it, I like what she says. Dena Kirkpatrick on bits for barrel racing