I broke a 5 year old QH mare a few years ago who hated a regular snaffle. Wouldn't listen to a single cue, ran through your hand, and had a generally bad attitude. Tried my straight/short shank Tom Thumb on her and she picked it up, perked her ears, and rode like a seasoned pro. I rode light handed and continued my other cues just as before; she just liked this bit better I guess.
All equipment, bits or no bit devices, are harsh in the wrong hands. I think a Tom Thumb is one of the more mild of the "advanced bit" spectrum.
My two cents. If your horse likes it, why reinvent the wheel?
Endiku the bit I have on my avatar is NOT a wonder bit. I do not use wonder bits because I do not like them at all. That bit is an o ring combination bit. I use it on Selena because she responds better of nose pressure than mouth pressure and it has really allowed me to be lighter and give her a looser rein when we are running barrels. Posted via Mobile Device
Ah, I'm sorry Sorrel. That's what it looked like on my phone. It looked like the lower ring was curved, which made it look like a WB.
Billy Allens are great, but they are expensive. I would recommend one too except for that OP is wanting something cheap. That would be hard to find cheap even used, since they have a good resell value.
OP, does your horse not work well in a snaffle or something similar? I like french links with rollers, personally, though I've had sucess with full cheek snaffles and such as well. I don't ride in curbs so I can't really give you any advice for those, though.