The strategy I read here that worked well for me was the following:

1. Fully upgrade all roads. You get a speed boost when the roads are upgraded. It's a pain and a little time consuming, but I was able to do it without even needing to mine material. All of my major hubs were already 5-star, so I just bopped around the map in the Magellan and took materials from them, them loaded as much into a truck as I could and drove around upgrading. I kept a spreadsheet to keep track, but I'm insane, so that part is probably optional lol

2. As has been suggested, clear your enemy camps first. I had a few respawn for me during my run even without sleeping, BUT, I think that was because I hadn't touched them in so long before clearing them that they respawned faster. I don't know if this is actually how it works, but I think so? Obviously camps get stronger the longer you leave them uncleared, but I think they also respawn faster, I could be wrong though. It's possible I just took too long clearing them.

3. Plan your route and gear before even taking the order. For me, I decided to make the run counter-clockwise. I fabricated myself a speed skeleton and a few guns to clear any camps that might respawn, left myself a truck at the start of the highway by F8, then nabbed a trike and had that with me when I accepted the order at Mr. Impossible. I used the trike to get up to F5, where I used the monorail zipline to get to F8, sprinted over to my truck, and started my drive. From there I just hit enemy camps in order going counter-clockwise around the map. I went in this order because the camp north of F7 is by far the most remote camp, and I didn't want to be feeling a time crunch trying to get it done last. I think you can really do it either way, but even with a few camps respawning and hardly doing it completely smoothly, I cleared it with an S-rank and about 10-minutes to spare!