I think you've probably got enough information on the TT so I'll just suggest a bit. :)
I got this curb bit
for my mare on the recommendation of a member here and I've found it to be wonderful.
The mouthpiece is solid so there aren't any confusing signals, the shanks are loose so -if she decides to "forget" how to neckrein- I can briefly direct rein without confusing her, and the shanks are pretty short and swept back so there's lots of "warning room" before the bit is engaged. It also makes a pretty good snaffle if you attach reins to the holes next to the mouthpiece (I do that sometimes if my mare is being especially goosey about "remembering" how to neck rein, I attach reins to both holes and go for it).
The one thing that can be disconcerting is that that bit rusts fast. Since it's sweet iron it's supposed to rust so there's nothing to worry about. You do want to make sure the rust is never sharp (and if it is, smooth it down with steel wool) but the rust itself is actually a good thing.