I'm definitely no bit expert (not even close), but I CAN tell you that I used to use a Tom Thumb, too, and I had a major problem with my horse throwing his head (violently) and sometimes even rearing, so I switched to a plain old O-ring snaffle, and he hasn't tossed his head or reared since :/
I've heard others complain about that bit, too...
I honestly think it's a horrible bit and I'd never put it in one of my horse's mouths again - but that's just my opinion and I've also heard that some horses go great in it. It's your choice.
I wouldn't use any shanked 'snaffle'.. (or broken mouthpiece) because, IMO, it's just a bad mix. Shanks + Broken Mouthpiece (no matter how many breaks) = Bad News IMO.