We had a similar experience with math facts, initially, and also used Big Brainz, but they didn't seem to like that until they didn't need it. Competition with other children appeared to help for #1, and competition with self (beat your low score for time required to complete a set number of problems) for #2. I also found that #2 was better with oral responding than written, as fine-motor was not a preferred channel. Now that 1&2 are fluent in all arithmetic facts, they want to play the apps I downloaded years ago for them, as well as the ones I acquired for #3!
It was helpful that we used SM, which, contrary to popular perception, has a fair amount of reinforcement embedded in new skills and concepts, which was perfect for conceptual learners.
The trampoline thing makes me suspect that the issue with math fact automaticity when not active is that he is using most of his mental energy on managing his body, and has little left to retrieve math facts. Executive functions are very closely related to math skills, and if he has to devote most of his EFs to maintaining attention and sitting still, he won't have enough left for math. Jumping on a trampoline is also a large muscle, rhythmic activity, which can be organizing for some kids with EF dysfunctions, such as ADHD. Also, the flood of dopamine that occurs when engaged in a high-stimulus activity can be described as "normalizing" attention, which now frees up the brain to do other things, like retrieve math facts.
Keeping in mind that ADHD or ED are only disorders if they have clinical impact (aka, get in the way of your real life), I would say, let him do math while moving--jumping, swinging, jogging in place, orally most of the time, and on surfaces with good tactile feedback and large writing spaces when written (e.g., chalk on a chalkboard, sidewalk, or driveway; stick or finger in the sandbox). Plus, he is only five years old, so needing to be in constant motion is not exactly unusual!
I would also wait to worry about his reading. If this is still his pattern in another year, then you might have an issue, but I would try hands-on strategies for reading and spelling first, and see if his reading resolves on its own.
