What are your suggestions for riders with very strong hands? While performing I tend to become rigid and pull very strongly on my horses mouth.

Try to ride with your thumbs down. Look awkward but in this position you can't pull.
Lunge lessons without reins.
If you tend to pull back when riding, you can use a grab strap. We use these usually for jumping because people tend to pull on their horses mouth, but it is good to have anytime because it is a reminder that says “kept your hands here!” We just use a stirrup leather and put it around the horses neck (the biggest part, right above the withers) Use this when practicing to create a good habit of where your hands should be. This might help when performing because of muscle memory? Not sure if this helps, but good luck!
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