I like using the eggbutt snaffle for flat work on the ground and use a crop to make my horse go. Personally, I don't have that problem about jumps but my horse is a bit lazy so for a bit stronger bit that gives you more control, I would use a rubber mouth snaffle and a twisted mouth eggbutt. If you have a trainer ask your trainer for advice on the riding problem and the bit. It might not only be the bit that is the problem. Hope this helped!
To start, I would use two bits, one for flatting and one for jumping. For flat i would use a soft snaffle bit and wear spurs or have a crop. When jumping ditch the spurs and/or crop and use him a little toughther of a bit. You will need to talk to a professional to decide the best but. One thing I would like to point out is the common misconception of a "harsh" bit. The boy is only as harsh as the hands that hold it. You could ride in a ton thum but and hardly touch the reins, or a snaffle and yank on his face. In this case the Tom thum would be softer for the horse. Just remember this and keep an open mind! I wish you the best of luck!