Please try this. Your next training session when it's just you and the horse, focus on asking the horse just once lightly to move forward with BIG energy forward. Doesn't matter where the head is, or how it looks. Just get that response. Keep your thighs off the horse, the forward comes from your calves. Your thighs block the forward energy. Keep the contact steady without gaps in the contact (so he doesn't accidently bop himself in the mouth).
Put both calves on lightly to ask for the trot and expect a BIG resposne. If you don't get a big response (and I mean BIG), then thump him hard with both heels (or use a whip if you need to). Piss him off, get a BIG response. (be safe though.. don't ask for more then you can ride). Ask ONCE. Then take your legs off and just ride. Don't keep your legs on, don't keep asking. Ask once, expect big and stop asking. If the horse starts out big but slows down, then you bop him with both heels for a big forward again and then take your legs off (i.e. Legs sit lightly on the sides of the horse but they don't grip, don't bump, don't keep asking). You'll need to re-teach the horse that he doesn't get to determine the speed or rhythm, and once he's in a gait, he maintains that speed and rhythm until you tell him to change it. He doesn't get to decide that for you.
Don't keep asking for forward. If you feel the horse is slowing down when you take the pressure off him, then get after him big quickly. You will probably need to really make him mad the first couple of times because he's going to want to ignore you. Get that response, then release the pressure. Be serious about this. Ask clearly, be clear in what you want. Get the response you want as quickly as possible and then leave him alone to do his job.
It's going to be ugly for a wihle. You're going to look like an idiot at first. Just accept that fact and focus on the problem at hand. Don't give up on yourself or your horse. Once you are consistent with what you expect from your horse, and your horse understands what is expected of him, then it'll take the lightest aids to get that big forward trot he'll need in order to move up in dressage. However, if all you've told him is that you're satisfied with a jog trot, then he's going to insist that you let him do that.