Driving to the USA in a rental car, TN in hand

I have a multiple entry TN visa. I'm going to load up a rental car with all my stuff here in Canada, and then drive to my new place in the USA, unload, and drop off the car.

From what I see online, I will need to fill out 2 forms, form 3299 and the Treasury Department Supplemental Declaration.

Aside from that, should I have any problems?

Will you have unaccompanied goods, or are you taking them all with you in the car? The forms are for goods that come before or after you.

If you're taking everything with you, and nothing is being sent by mover or mail or courier, you don't need any forms. Just a verbal declararion at the border will do, and just type up a list of your possessions you are bringing, just in case they search you. They rarely do though.