My horse can be the same. It helps to open your hands and start rising in the beat of the canter as I make my way to the next jump before sitting up as I near the jump and pick up slightly more contact before repeating my actions after the jump
If he's getting strong because he wants to go faster and therefore put himself into more work, then let him. I've found that holding horses back makes them want to go more, so if you allow them to make the mistake of putting themselves into more work, he will eventually realise that it's easier to listen to you and go slower.
It's really all down to making the wrong thing hard and the right thing easy. No bit is needed. My mare used to be like this and would gallop up to a fence. She's now a calm jumper due to the fact that I let her win in the first place, allowing her to gallop up to the fences rather than fighting her to slow down. However, it was important that I required her to continue at the same pace after the fence so she would eventually realise that if she goes fast up to the fence she will go fast after it - not have a break. Now she sees that it's easier to be calm since it requires less effort on her behalf. She rides in a hackamore - no bit needed.
If you choose to put a strong bit in your horses mouth, it will simply make him more resistant and fearful due to the pain and increased pressure it forces onto your horses gums. This will make the situation worse.
Good luck - I hope this helps!
It seems he is hanged ng on your mouth, you need to engage his hind quarters so he doesn’t pull, half halt is good. I don’t know anything about your horse but it seems like he is trying to be he boss and he isnt
Normally i try to stay with softer bits to start with and hopefully continue to use. But in that case i would upgrade to a stronger bit. For your safety it could be necessary.
You could get a stronger bit
Or you can start you lesson very softly and with lose rains and just practice the basics of turning ect. And if he pulls down let go of him, he most probably will become of balance and then get a small fright. He could avoid doing it because of the fright
Hope this helps💜