Teach him to ride on a loose rein so he won't always rely and lean on the bit
I have found that waterfords are excellent for this kind of stuff, paired with patience and lots of repetitive transitions
Ok if a horse if pulling your reigns they aren't accepting he contact and therefore hey aren't properly in the bit and collected. Make sure you're riding him with a steady even contact amd not pulling, this will encourage him to accept your hand and not pull. Maybe also if he pulls the reigns out of your hand give him and kick so he lifts his head, or give him a check and release (the release of the important part otherwise you'll get into a tug of war)
Maybe try a micklem or hackamore
My horse had a similar issue, gotta love TBs. He would "race at the trot", pull, take the bit, you name it. with him we did a lot of transition work but also using as little rein as possible so he doesn't really have the chance to lean. There was just enough contact for half halts but not enough to make him uncomfortable or enough to really lean into. Also try lunging and doing so ground work with verbal commands. Don't lunge him so he's extremely tired just enough to get his excess energy out and get him listening to you. The ground work with verbal commands will transfer under saddle so if you tell him whoa he will eventually figure out that means stop no matter what. As well as saying walk, canter, easy, etc.
LOTS of trot to halt trantions and halt when you fell he starts to lean forward
*and trot to walk and halt etc
First I would look into his physical condition. My horse used to do the same thing but we figured out it was due to an ill fitting saddle cause stiff shoulders.
Lots of half halts when you are trotting. Keep it slow but not so slow he's on the forehand. Focus on your rhythm in trot, if he starts to speed up, half half. Be careful not to use too much rein here because some horses will just lean back against the pressure. Don't brace your body against him if he tanks off.
Lots of transitions will help too. By getting his hind end underneath him it will help him lift in front. Keep him listening and focused. Walk to trot
Make sure you aren't balancing on the reins, he could just be taking advantage of you.