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I agree with Bob. However, if you want to discuss how you might apply the NFHS rules for adjusting the game clock to the shot clock...I think living with the reset is all you can do here.
"The referee may correct an obvious mistake by the timer to start or stop the clock properly only when he/she has definite information relative to the time involved. The exact time observed by the official may be placed on the clock." (NFHS 5-10-1)
You are obviously correct that you have definite knowledge that some time had to have run off. But what is required by the rule is some way to gauge "exactly" how much time ran off. Without having looked at the game clock, an official's count, or some other source of official information, I'm afraid you're stuck with the shot clock operator's mistake.
That's my take on how to apply the NFHS timer's mistake rule to a shot clock operator. NCAA rules for fixing a shot clock mistake when there is no monitor seem to agree (NCAA 5-11.4)
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