You could try AER. They rent out HD trucks, but I don't know about minivans. The airport companies may be your only option. There aren't many other places to rent here, and they can be pretty limited on where you can take them.
Might be worth it to buy a used one and then resell?
+1 on the roads. Most companies strictly ban travel on the Dalton, Denali, Etc.
I'm certain folks give it a whirl, but if something goes sideways you'd be super liable.
Not to mention I wouldn't want to run too far on either with junky, OEM rental car tires.
Our policy for work travel for the Dalton north is max ply, chip resistant with two spares for continued travel. (one flat means head back to base...)
If I was planning to put (edit: 700) miles on up there I'd follow a similar sop.
All of the big rental car companies expressly forbid the Dalton. Go North is expensive, Uhaul charges mileage. You just have to decide what fits your needs best. A crew cab truck from Go North might be your best bet.