I find this super interesting, and am only commenting on the NFHS section because I believe it parallels the NCAA PSK rules (as far as I can tell, at least).
Where I'm getting hung up, is HLinNC's point about K putting the ball next into play. They're only next to put the ball in play, as a direct result of a foul, and I agree with bama_stripes in that they are directly profiting from an illegal act. So from an enforcement perspective, are they really next to put the ball into play? That would not have been a given, because if they did this, and the kick still went through, they still wouldn't be next to put the ball into play (ensuing KO) and the foul would be declined.
Is this just a hole in the rule, where you can foul to stop a kicking score on 4th down and still obtain possession on downs, with only a marginal yardage penalty?
Same scenario, R74 slings K67 down to the ground by the facemask during the kick, and the kick misses. Same result - turnover on downs? I am wondering why teams, on long FGs, don't foul on purpose similar to the original scenario during the kick - there's no downside for R (they either get the ball if the kick is missed or blocked, with a small yardage penalty, and K has no recourse to rekick, or the penalty is declined if it is made).