I think that he is accostomed to riding this way, and it may have something to do with him being ridden in a Tom Thumb for a long time.
In any case, you will ultimately be trying to get the bit ti be associated with moving his legs. What I mean is when you ask him to bend or do anything, you want to be using one rein primarily, and you are actually talking to his feet when you talk to the bit. So, you want to lift the inside rein (say left) and as you come with more contact, he should first bend then go to where he is thinking of stepping his inside leg (left) under his body. In such a way you are talking to his hind end through the bit.
Right now, you aren't getting past his jaw, which he either braces up against the bit, or throws up his head to avoid it, either way you cna't get past his neck.
I would go into doing a lot of disengaing of his hind end and then starting immediately off into whatever forward gait you were in. Ask for a bend/cirlce when he braces, lift the inside rein, disengage getting that inside hind to step under then move off again. Pretty soon, I would think that just lifting the inside rein will get him to soften on that side and start to put his inside leg under his body.
Also, when you do halt him, make sure he comes to a complete halt and even takes one step back. I ask the hrose to stop, I look for a bit of give to the rein in both jaw and some in the body too, which you can feel as the horse shifts his weight onto his hind quarters. Might even ask for a step back or two, When you get it, give a total release, if you can.
I apologize if this explanation is vague. I am a little under the weather today and not sharp in the noggin.