Any recommendations for a bit a tad stronger than a hackamore? My horse tends to throw his head.

I agree with Laura. I'd say you should get someone on the ground to watch you jump and even video it for you to see and consider the fact that he is uncomfortable.
Hackamore is harsh when badly placed. Those with long legs are the strongest.
If he throws his head maybe he's in pain. Try to see if your using too much pressure. A stronger bit is not the answer.
Try to analyse and see what's wrong with your horse
Is he throwing his head because he is uncomfortable?
I recommend a level 1 myler D-ring
I recommend the Korsteel Copper and Steel Roller Snaffle Bit from state line tack.
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