Okay you can get a bit that will help LIFT the inside shoulder, no bit is going to fix her bending her head around and her shoulder still blowing out. That's a training problem, or a soundness issue. You need to get more control of that part of her body. Haunch turns, counter arcs, etc.
The TT as well isn't really good for gaming. I know you said you know about them already but I'm going to say it anyway just because. If your mare has a soft mouth then a bit like that really isn't needed. I would find maybe a short gag. My mare right now has a very soft mouth as well, but you'd be surprised how strong a truly good gaming horse can get. She right now has a short shank jr. cowhorse, it is a smooth dogbone with little copper rings in the middle. Just enough extra that I can take a hold of her if I need to, it lifts her inside shoulder a little better, and the gag gives a pre-signal to her before I actually get a hold of her face so I often don't even have to take up that much contact in the turns when we get going faster.
But you know, a bit is going to depend on the horse. If I had a choice I would actually have her in a Pozzi smooth dogbone lifter with a little longer shank because she is starting to really get a feel for things and is getting stronger and stronger. Not uncontrolled, but I sense when she gets rolling a little more on the gaming she will need something a touch more.
My cowhorse bit is this: Cactus Junior Cowhorse Bit Dogbone Roller
Mine is actually a slightly different, has copper rings around a dogbone instead of a legitimate roller, but it functions essentially the same as far as lightness goes.
Now this is the pozzi, what I would rather have my mare in at the moment: Brittany Pozzi Lifter Medium Dogbone - Horse.com
This is another bit I often use if I have a stronger, lifty horse. Rather than going up to a shank I will use the noseband and that touch of gag to just draw them back. http://www.tackstop.com/bitr903.htm
You could also bump up from a snaffle to a draw gag or loomis.
There's about a thousand different other options too. For other light horses I might use a sweet six iron wrapped lifesaver, a chain simplicity bit, a carol goosetree delight smooth, sharon camarillo tender touch..The beautiful thing about speed events is the flexibility and being able to choose from a wide range of things. As far as hackamores go I do really like a Little S.
On a side note sharon camarillo has just come out with a bit that I am dying to try. It's my favorite mouthpiece ever, with one of my favorite cheek pieces ever. It's called a trigger bit. http://www.barrelracingsuperstore.co...ge=&featured=Y