Ouch, that sucks. First thought, put a few small nuts (from bolts, not squirrels) in the handle's hole. Second thought, a short chunk of 1/4" pipe (or whatever) & likely a longer handle screw...more on those below. Third thought, grind that center round collar with the notch at the top down to the screwed-on escutcheon...Though, I think you eluded to that won't work. Which, brings me to my Fourth thought, use or try another handle from an old TV, Stove (not seriously, I mean come on what would people think) or of course a Sink Faucet for measurements & go buy a replacement handle to match the measurements.

Anyway, the nuts would only keep the handle from spinning but won't hold up well on the stem end & will eventually loosen, even with lock washers. But, the pipe could be crimped at the ends to fit & lock over the stem beautifully & lock into the handle just as well. The handle side will need some tweaking & maybe even a slit for shrinking.

Of course, the longer screw might still be needed...a screw from a door lockset might be just right in diameter, thread spread & length, if you have any spares around or are going over to the neighbor's for dinner any time real soon. Kidding...I'm just kidding...don't do that to anyone!