If you're not already going to be at Epcot or Disney's Hollywood Studios, then I highly recommend taxi.
I'm a big fan of Disney Transport. I've never rented a car for a Disney stay and I never will. But I'm willing to pop for a taxi every now and then (no more than twice per trip) if it will save a lot of time. And going from Polynesian to a BoardWalk-area resort will take a MUCH longer time by Disney Transport than by taxi.
I know, I know, taxis aren't cheap. I hate to say it, I hate the way it sounds, but as a past guest at the Poly I guess I can say it without being offensive ... if you can afford a room at Poly then you can afford a taxi.
We took a taxi from Poly to Beach/Yacht Club when we had an IllumiNations cruise reserved. And we took a taxi back home to Poly afterwards. Very glad we did it that way.