As a Jax main...
Gut his overbearing stats but keep him unique. Let me explain. Reduce his hp, armor, and magic resist per level. So you actually need to build defensive items to be tanky. Reduce the armor and magic resist you get from ulting, but increase the scaling so you're not super invincible if you're behind or building tank items. Reduce ult passive damage, but increase the scaling. Increase q scalings. This way you can't do insane ap damage without any ability power in your kit. Increasing q scaling should keep the ult nerf relevant but not devisating to Jax. KEEP THE ABILITY TO DODGE AUTO ATTACKS. That gives him outplay potential, but reduce the maximum amount of time he can dodge autos from 2 to 1.5. It won't hurt his jungle survivablity much but he won't have a whole 2 seconds to be basically unhurtable if you're an attack based champion fighting Jax.
Maybe these are too many nerfs, but I feel like Jax needs them. A good Jax can easily abuse his current kit too well. If Garen and Yorick is getting nerfed for stomping low elo, Jax should also be nerfed.