PABlue wroteNow YOU call up NFHS and tell them they are wrong because they are not listening to PA.
Well, since I don't umpire NFHS baseball, they won't listen to me either.
Here's what you quoted in the OP as coming from "NFHS":
PABlue wrote"Because once the CR replaced the catcher...
That's their first mistake. The CR did not "replace" anyone. He simply ran for the catcher as a courtesy runner. By "NFHS"'s own definition of Substitution (2-36, Article 1), a player who replaces another player in the line-up is considered a substitute. A CR is not a substitute because the pitcher or catcher they run for remain in the line-up. Their use of the word "replace" is careless.
PABlue wrote...the catcher can not reenter for the CR in (that half-inning) Pg. 93 CR# 3.
"NFHS" is taking the language in CR#3 out of context. It is meant to apply only while the CR is still actively running for the catcher or pitcher, not the entire half-inning. Once the CR is done running the bases (because he either scored or was retired), he returns to the bench as a player not in the line-up. But somebody has to occupy that position in the batting order. It cannot be the CR since he was never a substitute, and since the CR rule says the catcher was not required to leave the game, that puts the original catcher back in that line-up spot.
PABlue wroteNeither could the CR bat in that position due to the fact the CR can not be used in the same half-inning.
Again, very careless language. The CR can be used in the same half-inning...as a CR again!
PABlue wroteTherefore, the team would have to use a pinch hitter until the half-inning is over".
So, this convoluted argument results in the original catcher being required to leave the game when a CR ran for him, which is in direct conflict with the CR rule.
Nice try, "NFHS". Play again some other time.