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There are two separate statements in that rule:
"A period or periods may be shortened in any emergency by agreement of
the opposing coaches and referee."
Last year I had a 2nd quarter that ended with 35 seconds left because of a player injury that necessitated calling an ambulance. Two years ago I had a varsity game that ended with 1:20ish left due to an ambulance call. I'd say these constitute "emergencies" for purposes of this rule.
"By mutual agreement of the opposing coaches and the referee, any remaining periods may be shortened at any time or the game terminated."
No emergency required here. If the two coaches agree to shorten the game in whatever manner they wish, I'd find it highly unlikely that the referee would disagree.
Rule 1-7 mentions allowed state association adoptions.
8. Establishing a point differential to terminate games or to use a running clock when the point differential is reached. (3-1-2)
If the state association adopts a running time or ending of game rule, that's completely in the purview of the state association.
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