There is no conflict. The team member who is on the bench in your Case Play has not been DQ'd, but that doesn't automatically make him an eligible substitute. In this case, a specific substitution rule forbids his entry at that point in the contest and he is therefore an ineligible substitute. Thus the team has to continue with four until he becomes eligible. That isn't a difficult concept. You just don't like it, so you conned the NFHS into overriding a rule in order to do what you desire--allow a team member to return to the game improperly.
As for the TF situations prior to the start of the game, the RULES contain specific exceptions to allow for substitutions in those cases.
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