Your question is a complex one and one that is in the minds of many good horsemen when horses are not going as well as we would like. Since horses can only convey how they feel through body language and their attitude during and after work, we are often at a loss to know exactly what is going on. The body is complex and often a problem that originates in one area is only visible to our eye when it creates a problem in a different area. The musculature, especially in the back, is difficult since it is impacted by both the stress of more or different work, as well as by the way of riding and training.
Horses that are worried about jumping often begin to ‘rush’ to the jumps in an attempt to get away from a rider’s interference, or even a general lack of confidence. When horses hurry the last few strides, it quickly becomes habit for the horse. Like any habit, changing it takes far longer than creating it in the first place! I’m particularly impressed with how you dealt with this issue. Cantering toward the jump, and then doing a quiet and organized transition to trot just before the point the horse typically rushes, is my favorite exercise for this problem. Adding smooth and soft turns over the jump, first from the trot and then in canter, is a great next step for the horse to learn to listen for your direction rather than hurrying the process and rushing off after the jump itself.
As to your horse feeling different after a somewhat larger school, just as you’d feel the difference if you went from simple exercise directly to significantly more strenuous training, your horse is liable to feel the same. I prefer to build up from starting your gymnastic very low each day with a gradual raise and spreading of some or all of the jumps to the point the horse is trying a bit but still comfortable. It is a good idea to finish with one time through the line very small again so that your horse returns to the barn with a feeling of success rather than a big effort.
With a horse that tends to have some muscle soreness, I like to do some jumping most every day, even if it is just ground poles, and put a flatwork day in between two real jumping schools. Just as human athletes use this technique of doing different work on alternate days, note that, unless a real injury is involved that will only heal with total rest, giving a horse a total rest is not in their best interest. This is especially true with horses that are stabled for all or most of the day rather than having significant turn-out time in a big enough area to be able to really move. Also spending time working ‘long and low’ at the beginning, the end, and during breaks in your training I feel does a lot for virtually every horse by stretching and strengthening the long muscles. With a horse that tends to hollow or invert their back, this is the place to use lots of leg to insure that your horse’s hind quarters work well under you while the back is stretched. Pay most attention to the motor under you rather than the head and neck in front. This develops the strength to use these muscles effectively when the horse is in his working posture for jumping.
A final note on this topic: each individual horse has his own natural technique when it comes to jumping. Trying to insist a horse approach a jump with his head either lower or higher than is natural to him is often the cause of tension and resistance. Hunters need to gallop and jump in a particular style and it is seldom satisfying to either horse or trainer/rider to try to make a horse go in a way that is not natural to him. Jumpers are not bound to a certain style and some are very capable competitors even when their particular style is far from our “ideal.” Be sure that you work on balance and adjustability on the approach to the fence while allowing your horse to figure out what works best for him to deal with both tight and long take-off “spots.” As a horse’s balance improves and he learns the importance of landing as well as taking off in balance, the jump will also improve. Virtually every horse can focus best on the act of jumping when he is in a focused yet relaxed state of mind. Either pain or irritation will only interfere—whether it comes from a poorly fitting saddle, too strong a bit, or a rider whose balance is constantly shifting at the wrong moments! I find it rather amazing that so many horses find ways to cope with discomfort and even pain. They truly are remarkable animals, generous in so many ways.
Congratulations on being the sort of horseman that uses that all important “aid”—the one under your helmet! You are aware of every aspect of your horse and seek solutions that are most likely to benefit your horse. Not enough riders and trainers think in this way and are quick to go to more bit and/or draw reins for the quick, but temporary, fix.