We do fun little hunter on the flat tests. Counter canter, hand gallop, flying changes, simple changes, extended trot.... etc. memorize a hunter flat test and go around like you're showing. Makes for a much more eventful hack.
Work on extending and collecting each gait. This will help improve his jumping. Start at the walk. You can put poles on the ground to help you. I don't know how big your horses stride is but watever is normal, place poles to shorten his stride, then to lengthen it. Do this at the trot and canter as well. Soon you will be able to do it without poles. This helps when jumping to get the horse to the jump corectly and to add and subtract strides in a line.