Looking for a bit (that is dressage legal). During our ride, my horse will get really heaving in the hand and then start opening his mouth to get away from the contact. Any suggestions?

Not necessarily the bit sometimes. Roll your hands back towards you and lift them, have your horse release pressure, but a Myles with a port sounds good too
Myles with a port maybe
I would recommend Myler comfort snaffles on him. They distribute pressure really well and are comfortable with many different horses. They are gentle but you still get good contact and they are dressage legal.
Myler bits could work well with him
He has been in a French link eggbutt snaffle and I have also tried a Mullen mouth eggbutt which helped a bit but he is still really strong in the hand
Opening of the mouth and getting strong in the contact is your horses way of telling you that he is uncomfortable in his mouth. It would be useful to know what bit he is currently riding in, since different bits work in a variety of different ways and will therefore affect how your horse rides in it. A single jointed snaffle, for example, works by putting pressure on the bars and roof of the mouth, as the single joint provides a nutcracker action, pushing down on the bars and pushing the joint towards the roof of the mouth (often resulting in head tossing).

A lozenge and french link work more on pressuring the bars and tongue, though due to the french link's larger surface area the pressure is more evenly distributed across the tongue, so some horses may find this more comfortable compared to the lozenge which concentrates more pressure on the tongue.

All I can suggest is to change your bit to something lighter instead of something stronger and work from there. Look at the action of your current bit and try something with a completely different action which works on alternative pressure points within the mouth (tongue, bars, lips, etc). Although my mare rides bitless, I know she hates the action of a snaffle since she has a low palate so the single joint puts too much pressure on the roof of her mouth. However, she does go well in a happy mouth mullen bit, which evenly distributes pressure across her tongue rather than the bars and roof of her mouth, which just goes to show how much your horses mouth anatomy affects his comfort.
Hey Emma
On my horse who does the same thing I use a rubber mouth price snaffle
Hope this helps
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