What about that new contraption that Myler makes? I saw it at the equine affair in Springfield Mass last year. It's about $150. It's a combination thing and uses a myler bit. Maybe it's the same one that Spirithorse is talking about. I think it has 4 pressure points other than the bit. When you take hold of the reins, the pressure points do their job before the bit ever comes into play. It gives the horse a chance to respond before bit pressure is applied.
For a TB, I definitely would not go with a fatter bit. Most TBs have fat tongues and not too much room for a big bit. My TB doesn't salivate much either, but he does seem comfy with a D ring french link. He's not a head tosser, so I can't comment on that.