Heather decided Pilgrim needs to appreciate me and my generous and light hands more. His bracing and popping on the bit when he gets tired of working in frame (while has dramatically reduced recently) is still a problem during rides and is causing me to compromise my riding position so I can focus on him. We decided to lunge him side reins so his only option is to relax and go in frame. She tried starting him in stretching frame but he just went around with his nose in the air, so she put him in working frame. After he tried evading the contact by sucking back, running out and blowing up....he finally realized that they don't give (unlike my hands) and his only way out was to just relax. It worked wonderfully. After a few times around each way with him softening and relaxing, we quit. It was nice to see him get it, and it should definitely help when I go to ride him. He has to learn he can't take advantage of me, has to have some kind of bit acceptance, and there has to come a point where every ride is not a fight and we can actually work.
The video at the top is when he understood what we were asking. Below is when he was still trying to figure out how he could avoid it and finally relaxes a little at the end: