Thanks for the comments and questions!
Yes, it is wise to have 2 full spare tires for trips like this, but we only carried 1 because weight and space are always an issue. However, if I were to do it again, I would consider taking a 2nd spare tire but without the rim and put it on the roof rack. That way I know that if I get to a tire shop, all they need to do is replace a destroyed tire on one of the 5 rims... That way I don't depend on the remote shop to have "my tire" in stock. Of course, this still leaves you in a hole if you get 2 flats and you can't fix either before you get to a tire place. However, the following helps:
1. Have good tires and decent tread at start of trip. I know there are many options, but we have BF Goodrich AT KO2.
2. Air down when on long gravel roads... the 600 mi on the Dempster (one-way) definitely makes it worthwhile (reduced probability of punctures, a bit more comfort and also grip). I think I varied between 45-50 PSI on front, 50-55 PSI on rear.
3. Carry a tire repair kit (We have an ARB set). Combined with an air compressor you may be able to fix small punctures while leaving it on the vehicle and not using the 1st spare.
4. Go slow! This is probably the most important recommendation that reduces your exposure to trouble. If you skid or if you get into softer shoulder it may result in flats ... or worse (see image below of someone who wrecked). Also, there are not only potholes but sink holes. Especially where culverts have failed and undercut the roadbed... you may be the first to find out there is a sinkhole that has not yet been marked! The roadbed is not thick enough to keep the permafrost, then culverts sink, snap, and cause erosion from underneath. Climate change doesn't help... we are always behind with how we build things vs. how we should build things.
5. The road, especially the edges, gets soft when it is wet. Consider waiting a day or so for things to dry out to reduce probability of problems. Shale is more problematic when the road gets softer when wet and results in increased probability of puncturing side wall (no repair possible).
6. When traffic comes from the other way, slow way down, carefully and slowly move to the edge of the road... you can easily loose control in a soft shoulder!
That said, we had zero flats out and back to Montana, well over 6000 mi in total, and probably 2000 mi of gravel and dirt. We did help 2 others change tires (see an image below).
TIME SPENT ON DEMPSTER
We took 14 days on the Dempster. You can do it in 2 days up, and 2 days down (4 days total), but what is the point of that? The 14 days on the Dempster included 4 days backpacking in Tombstone Territorial Park, which is an incredible mountain range... straight from Lord of the Rings!
Word of caution... The Dempster is 1 way in, 1 way out. A semi-truck had too tall of a load and damaged the bridge across the Eagle River... which was then closed. Light vehicles were allowed to pass through intermittently, including us. Took 10 days for full repair. Alternatively, drive back several hundred KM north to Inuvik, take flight home, pick up vehicle next year... so... it is good to not be on a tight schedule. We were only camped for 1 night on the north side of the damaged bridge... If you have a Unimog of MAN overlander you may have had to wait 10 days...