If it were me, I would email the maker of the jack, explain the problem, maybe even a pic or two, and maybe they will send you a new cover. All it takes a is a little computer time.
Worth a shot, before towing 2 hours round trip, for a 10 minute part swap.
Now I am assuming the cover is just help on with a few screws, not all jacks are created equal.
2012 Ford F250 ext. Cab 4x4
2002 Jeep Wrangler Sahara
2008 Yamaha V-Star 650 Classic
2008 Work and Play 18LT