I've run for months and months and maybe years with out-of-state tags, but never lived in a vehicle property tax state. I wouldn't deliberately drive on expired tags, and the property tax thing looks like it'll be a possible problem.
You know the address where you're going, right? Register the car there. You should be able to find a license plate agency that typically deals with fleets to do it for you. I once put FL tags on a car before I moved there, when my employer transferred me from MD. I registered it at my future work address, IIRC. No drivers license required. This was pre-9/11 though. Oh, and I ran a truck fleet for my job so maybe I had a prior relationship with the agency... I dunno.