The single most important thing to realize is that the impingment is not due to the vertical forces exerted by the floor on your feet and transmitted through the legs up to the hips.
The impingmente is actually due to too much of a hip flexion (raising your legs to step on a big rock for example). the following video, at 2:30, shows how it happens:
When I was diagnosed with FAI 4 years ago, i stopped running and began cycling in order to maintain some aerobic fitness. Worst thing i could do, because hip flexion, especially on road or TT bikes, is much larger than when running. I also did endless hours of physiotherapy aimed at strengthening hip stabilization muscles, which was good, and stretching the hip and thigh muscles, which was absolutely counterproductive. Let me explain why.
There was, and still is, a small tear in my labrum, with inflammation around it, which was the source of the pain. When cycling, i was applying force with hips flexed, and that contributed to worsen the inflammation and pain. Furthermore, stretching hips and thighs tended to pull the tear sides apart, enlargening it and difficulting cicatrization.
I visited then, like, the fitfth or sixth doctor, which finaly gave me the solution: “stop stretching and cycling; start running slowly on flat courses or swim and come back here within a month”. Strange enough, but i went for it. My pain simply went away. The secret was just stopping to apply forces with flexed hips, wgich compressed the joint, causing inflammation, and quitting stretching the labrum tear, leaving it free of tension to cicatrize and therefore recover. After one month i could already get back to running on steep trails.
Every case is different, but i hope it helps. Remember: the impingement is not due to vertical impact, but to hip flexion. Good luck!