I actually have the same trip planned, as a matter of fact, I was supposed to go last year. Elderly parent stuff ......
I am just throwing my thoughts out there as there is no right or wrong ......... generally speaking.
I would stick to stock size tires for this trip. With the 285's you will take what I believe is the biggest hit on gas mileage next to the roof top tent. You will be driving a LOT of miles.
With that said, a "hard shell" RTT will also cut down on the gas mileage loss over a "conventional canvas type", as it is much more streamline.
The gas savings alone over a 10000 (possibly more) mile trip will somewhat offset the higher cost of a hard shell RTT. The "bad" tradeoff with a hard shell tent is the smaller size when it is set up.
Ease of setup and takedown should be considered as, at least for me, it is going to be a daily event. The hard shell tent wins here.
For what it's worth, a friend of mine did this trip 3 years ago. When he got back he made it very clear that he hauled "way to much stuff" and that his next trip up to Alaska would be with a rig "similar" to mine/yours.
As always, Your Mileage Will Vary (pun intended)