Tasia, I ask about the bits, because I wonder if the tongue twisting is coming from discomfort in the bit, particularly if you say he doesn't do it in the Myler. It is possible that he is being pinched by a part of the bit when you take up contact on one side of his mouth. It is also possible that the shape of his mouth does not accept the type of bit you are using, it could be hitting him in the roof of his mouth, putting undue pressure on his tongue, or pinching his tongue.
There is nothing wrong with snaffles - most horses will go very happily in a mild snaffle, whether single joint or linked. FEI dressage horses *should* go happily in a snaffle if trained correctly. It is just that some horses mouth conformation and personal likes/dislikes lend themselves to the use of other bits than the simple snaffle. I know my little wb gelding is terribly fussy in the mouth, he chews, draws his tongue back, shakes his head etc. and has done so for many years before I started working with him.
Unfortunately sometimes you need to bite the bullet and just pay the money for a good bit. If the horse goes well in a Myler, and you can't get him happy and quiet in the mouth, in a snaffle, then I would be thinking of whether I want my horse to be relaxed, submissive and acceptant of the contact when I ride, in return for an outlay of money on a good bit. Or, also slightly resistant, backing off and not terribly happy, in a cheaper bit.
I know that I'd rather pay the money. I'm currently between jobs, have 3 horses, a car, a dog and a general living expenses to pay for, and I've still gone out and spent a lot of money on a bit that my horse seems to go much happier in.