Regression discontinuity questions
The fact that your outcome is measured at a later point in time than the treatment is not a problem, and not unusual either - this is true to some extent in all RD studies (if this were not the case, there couldn't be causation). 

As for how to analyze your outcome, I suggest a couple of different specifications. First, you should use the continuous fine measure as an outcome. Second, you could use an indicator variable equal to 1 if they got a fine, and equal to zero if they didn't. You might be able to do similar dummy regressions for the more/less cases too, but that's a little more complicated. If you want to be a little more advanced, it would certainly be interesting to take the RD framework to a tobit model. Shouldn't be too complicated, I expect, but I haven't thought that much about it.