Pick the foot up and put the foot down cue shouldn’t mean you stomp the ground. If you are doing this right you should just be able to start on the spot and then gradually pick up speed with your feet getting lighter the faster you move. Its more pick it up and put it down rather than stomping or thumping the ground.
Sometimes people with very arched feet can collapse quite significantly if they can not handle the eccentric loads under speed. You may find standing that you have high arches and don’t collapse but as you run they collapse as they can’t withstand the forces. Possibly a visit to the podiatrist might be a worthwhile step for a screen to assess the need for specific foot strength exercises and or orthotics.
Vertical jumps arguably tend to correlate better with acceleration when the time you have to produce force is longer. Its the quick contact exercises that will correlate closer to your top speed running if this is where you are having the issues.
I think you may have a number of things to look at. Just work through a check list and tick them off. You may also want to get some footage of your running from in front, and behind to see what your feet are doing on ground contact. If they are collapsing regardless of what you try technically then you may have a structural and or strength issue to sort out.