Judge Cawley has been pretty clear that he'd like to see you take a course before you apply. I expect applying for restriction removal without the course would result in denial with a suggestion of courses to take.
While I do not think there would be harm in trying - Cawley has consistently come across as very fair - I do not think you should. We have a nice, crystal-clear path to unrestricted permits... take it. A little bit of patience will pay off in spades.
In the meantime, if you feel it's really necessary, there's nothing legally preventing you from carrying right now. You already have a concealed carry permit, albeit with "restrictions." Restrictions are extra-legal (meaning they are not part of the law) and you cannot be charged with a crime for violating them. In theory, a licensing officer could suspend your permit if you were caught, but that would require a lot of things to happen first:
1) You'd need to get caught
2) The officer would need to care enough to report it to Cawley
3) Cawley would need to care enough to do something about it (and be willing to subject NYS to the potential legal ramifications)
None of these are likely.