Wizard,
The amount of memory space occupied by a twelve foot or so fall is way out of line with the time the fall takes. So many quick acting experiences are that way I suppose. One broken bone, wrist, I finished my job and made the hospital about six hours later. Made it difficult to change the diapers on my just born son. Hmmm. There were some advantages after all.
Better choice I believe keeping the tire low. Don't go after the spare if you have to jack up to get to it. Find another solution. Perhaps drop spare, attach tug rope (or vicee versee), then jack, then drag out the spare.
I've got a crippled ex-brother-in-law with one eye who is proof you don't crawl under a jacked vehicle. Stupid Navy orders on a ship at sea.