Why I asked was that there are these things called "gray horse melanomas" (basically harmless tumors, unless they are interfering with life functions) that all gray horses eventually get, some get them sooner than others.
A very common place for these melanomas to crop up is in the corners of the mouth (my gray mare has them there). When they're in the corners of the mouth, they seem to really impinge upon the horse's ability to feel any sort of jointed bit. The horse, in my experience, starts leaning on the bit, rooting in response to hard bit pressure, and generally just being kind of ornery about bit cues.
With my horse, at least, she's terribly dull and lean-y in any jointed bit but put a solid bit in her mouth and she's super light and responsive.
That's why I ask, it sounded to me like your horse was displaying "classic" symptoms. I could be totally off base, of course, but check the corners of your horse's mouth. If they feel hard and kinda lumpy, you've found the problem.
I haven't tried a mullen mouth snaffle on my mare yet but I have found that she really enjoys a ported pelham. I stick on on her and just attach a snaffle rein, no curb rein, and she goes along quite happily and very lightly. Of course, for showing, a ported pelham with just a snaffle rein probably wouldn't cut it.
Basically, any solid mouthpiece (if the melanomas are his problem) is going to be the ticket for you two. I'd stay away from leverage bits that give you no option to not use leverage, like a kimberwick, if possible just because you don't want to be accidentally encouraging false collection.
Good luck! :)