It would seem that allowing for me to go 2 weeks prior to the beginning of classes might be a strategic move; they really wouldn't have much time to drag-ass on the RP once school starts.

That'll be fine. Even if you have to teach without an RP, it would just be for about 10 days at most. Not worth making a fuss about, imo.
But if you were to arrive just before the teaching begins, that would give them more time than they actually need to drag their heels re your RP. Generally speaking, university FAO's are rather lazy, and dislike red tape. They prefer to visit the local PSB office only once with all the paperwork necessary to apply for their foreign teachers' RP's. So, they wait until the last of the FT's arrives and has proved his worth in the classroom before applying for the RP's on behalf of their foreign teachers en bloc.