Have you tried longline lunging, I have been doing this with my youngster, and what a difference its made to her. I haven't yet longline lunged off the bit, but attach it to the head collar side rings, I use a roller and have added a loop of baler twine to the side rings, so the reins aren't quite so fixed, I found that the outside rein has made such a difference to her, and especially with it coming round behind her bum, makes her carry her self as one instead of front legs and back legs.
I do use side riens, which I attach to the bit, but I have also added a loop of twine to them as I found even though they are full size they were too short even on the largest size. I know people will say that when they are so loose they may as well not be used, but I have tried her with and without them and find that that little bit of weight on the bit just encourages her to seek the bit, whereas without she just points her nose out front and she seems to suck the bit back over in her mouth, making it hang off the bridle at a strange angle, yet loose side riens stop this as I've said just by the light weight of the side rein.
I also hate anything which forces a horse into a contact or outline. I have found that concentrating on the walk is always best when riding, if they tend to hollow, getting them to accept your legs and hands, without evading, and building up topline muscle slowly, lengthen/shorten stride, good halts - where they halt underneath you with just a squeeze/release of the rien and tighten your seat muscles. Lots of changes of rein, leg yield, turn on the forehand, lots of exercises that involve leg to hand riding. But mainly looking for a nice relaxed horse that accepts your aids and stretches down seeking the bit.
Once the walk is good and relaxed, then I'd start to introduce trot, but depending on the reaction, I'd only look for a few strides at a time, then back into walk.
Please don't take offence, but 30 minutes of trotting round with his head in the air is allowing the muscles that you don't want, to get stronger, slowing down, and asking him to carry himself, will encourage him to build the muscles he needs to carry himself and you.
One other thing I do is carrot exercises, stand at his shoulder, and offer him a carrot, so he really has to stretch round to you to get it, also offer him a carrot from inbetween his front legs, so he has to stretch down and under to get it. Start so that it is quite easy, but if you do every day, you can make him stretch just a little further each time, you'll be surprized at the stretch and balance that can be built up, over quite a short space of time, and this is one he does all the work!!
Hope this helps
Lesley