I've got a horse that has been in regular work for about a year now. She has always been a "heavier" horse as far as wanting to really lean on my hands and the bit. I've patterned her and have made about 12 runs on her so far. When I am just exercising or schooling she gets a lot worse, she tends to want to throw her head up, lean on the bit and just run through anything I ask her to do. I've gone back to riding in a snaffle and do a lot of lateral work and rollbacks off the fence, so I am just sort of hitting a wall here with her. She is not nearly as bad when she is running, I don't know if its partially an attitude thing or what. I'd prefer to find some exercises to do over switching headgear or anything but I am open to suggestions. I've been riding her in a snaffle/martingale lately and she runs in a goosetree simplicity chain. 

I have had good luck when I go back to basic horsemanship. I do a lot of the Phil Haugen level one exercises such as the correct one rein stops to get a horse off the bridle.

From my experience, and what I have been taught, a snaffle bit is not always the way to go for a heavy horse... but I do go back to basics. I do A LOT of ground driving with one that wants to be heavy. I also check teeth, hocks etc because being sore will make one heavy in a heartbeat. Your horse sounds like a prime candidate for one that is sore. She might be gritty when you run her but slow it down and she wants away from it.

Is she sound? I know mine will get heavy on the forehand if their hocks get sore.

Use a short shank correction mouth bit with the training ring on the side.using a draw rein. Ride in a safe flat field or safe trail. Do one rein stops randomly and often  working both sides. Stop . Sit . Hold the rein bringing nose to side and hold till horse stands / relax then release. Ask for back, stop. Side pass , walk on. No running or trotting for a week.. no barrels or arena . Go somewhere on a trail walk ask for the one rein stop, back, side. Repeat often and never move forward until a full stop and give.the following week pick up the trot. When you are doing it right your horse will start talking to you verbally. Saying he has learned it. At this point you can use a snaffle for anything.