I had a similar issue this past year for 4h. But, I ended up dropping the Western showing and just went with English (only because I ran out of time to train XD). As I switched from a Dr.Bristol english bit, to a low/medium port shank. Lets just say my mare was confused! That's why I dropped out of the idea, ran out of time to get her used to it. I watched some of the western classes at the fair and I could have sworn people were using Tom Thumbs. Now, when I rode my mare (well, I leased her..) western, I used a TT. She understood it. The only reason I didn't use it as a showing option, is because I thought we had to use port bits. Guess not.
I think you could use a TT. Unless the rule books says you can't, I say go for it. They never checked out our bits, except for Gymkhana.