Anyway, my girl only gaits well in contact too. Kind of weird for me because I am used to trotting horses and backing them off the bit by bumping them a tad so I have very little contact. I had to learn to ride my Fox Trotter different from that if I wanted her to gait at all. Even at a walk, when I normally ride with a loose rein, she will still sometimes weave all over the place like she doesn't know how to travel a straight line unless the rider is holding her in that position. But I still strive for a loose rein at the walk.
She also hates any bit with a broken mouth, whether it is a plain snaffle or a broken curb. Sure, I can ride her in a snaffle, but she doesn't do her best in it.
I have a mentor of sorts who also trail rides gaited horses and she only rides in a short shanked curb with a solid mouth. And that is how my mare rides best too.
I don't know if it is how they are trained, or just because that is what it takes for them to gait well, but it does seem like at least the Missouri Fox Trotters I know do better riding in a curb with contact. Two handed seems to work better than neck reining. I don't know if that is just my mare or most of them. My friend rides two handed also. It's not that you can't neck rein them. It's just that I have had better luck two handed when gaiting, even with a curb.
I was so afraid that my mare would go lame from traveling "hollow" after all the research I did on the internet that I was almost afraid to let her travel with her head up and nose out (which is how she likes to gait). But I've come to peace with it because I think she is more neutral than hollow and I do practice collecting her at the walk and we canter now and then too. Mixing up the gaits is supposed to help counter-act the damage that can occur by gaiting in a hollow frame. Anyway, I guess I better quit babbling on and on.