When using the Prius jack to change tires, I found that the base was too small for good stability on a dirt/gravel road shoulder, and the jack handle was both flimsy, awkward, and required decent strength to operate, especially when it was in the "full down" position. So I cut the metal top of an old shop light to a 12-inch length and screwed it to the base of the jack with sheet metal screws in the four locations indicated by black dots in the pic below: To replace the jack handle I bought a $.98 threaded hook, locked 3 nuts together on the threaded end, and bent the hook end more sharply so that it just fit into the metal eye of the main threaded rod in the center of the jack--that new hook can be seen dangling from the eye on the right in the picture above. The locked together nuts can be driven by any 13 mm socket, so I can now use either a simple 1/4 inch ratchet or my DeWalt power drill to raise or lower the jack. (picture below): I think this system is more easily used by those without a great deal of upper-body-strength, which would a substantial number of men and women, and DW in our case.
Nice improvement, well done and thrifty. After one use though, I tossed the whole factory kit in the garage because it's unsafe as you discovered. I keep a floor jack, Dewalt Impact, 6-point deep with adapter, cross tool, gloves and scrap of dense foam for the knees in the back now...but that's me.
I've carried a scrap of wood in the trunk of many cars just for the unstable surface issue. An old shower curtain to address the "it always happens in the rain or snow" problem,
It doesn't have to be on gravel to slip. It slipped on my concrete driveway just after I got the weight off the tire.