The cops sit here ALL the time and yes it's a $$ raiser.
There is a difference between challenging the fine and asking for special driving circumstances for work. You've admitted fault already by paying the fine so no, don't bother challenging it. You just wont win. It's only 3 months anyway, it will be over before you know it
Rather, ask for a drive for work restriction thingy. If you've not been suspended in the past you'll most likely get it.