Some of the penalties I've heard of for bicycle stop sign violations don't seem to fit the crime. Esp. considering that many, many stop signs are placed for purpose of speed control than any other valid reason (I think at least 75% of the four way stops in my area could be reduced to two way stops except for the fact that would probably at this point confuse people so much that there'd be in increase in accidents).
Anyway if it was up to me and I was a traffic cop, I would issue tickets depending on factors like whether the cyclist slowed enough to have stopped if he had to and if he generally seemed to be situationally aware. Much as I think many stop signs shouldn't exist, blowing through one at speed is provocative and I'd ticket for it.
Giving police no discretion and ticketing someone an auto type fine for riding 5 mph though a sign will simply make some people give up riding and take to their cars. I don't see how that's a better solution for anyone. I'd advocate small penalties--maybe $40-50 (w/o added court fees) as a way to adjust people's behavior w/o making them feel like martyrs for infractions.
Sorry I have no advice on getting a fine reduced. Getting two in two weeks probably isn't going to help you here...