I can't understand why they aren't adjustable, or failing that why nobody has come up with an adjustable aftermarket headrest.
I can tell you this, with the stock headrests in their normal position, I can't drive the car for more than an hour or so, and during that hour it is increasingly uncomfortable. If forced to stick with it, I would need a chiropracter appointment the next day.
Reversed, there might as well be no headrest there at all, it's so far back and away that any damage from sudden acceleration is going to be done by the time my head reaches it.
I guess I could do a jury-rigged towel wrapping deal like you describe to get it into the perfect position. BUT my 6'4" son would require a different setup, and my HGF, who puts the seat in a very different position even though we are in the same height, would require still another.
Something that would flick into different angles with the same ease as the seat itself does would take care of this problem, but for me, the answer is to ditch the headrests and hope for the best... and it just so happens the standard headrest in standard position fits my son perfectly, so I keep one in the hatch and he uses it every time, whichever seat he is in... especially if he's driving.