I have the same land and back issues. The sidewalls on most mower tires are so stiff that lowering the tire pressures is not go to help you that much. Besides, most mower tires are only inflated to ~12psi anyway. It may help a little, but it won't really fix the problem.
1. First place to check is with your JD dealer. Lots of users have similar back issues, and the manufacturer may offer an option that can be fitted to your existing seat. Exmark offers such options for their mowers.
2. Failing that you may simply need to buy another model mower that comes fitted with better seat suspension. Exmark has the Radius-S with the seat independently suspended by 3 soft shock absorbers... but you may not need a 48" mower. Surely JD offers a similar model.
Thank you for your service.