How can I get the White Western Star back to the garage for the Fixer Upper task?

Shorter (by distance) route

There are no true shortcuts in this game. Figuring this out took me about 3 hours. However, it is absolutely possible to get up the hill to the West. Here is the route I used with points of interest labeled:

First and foremost, you will need to fully repair and refuel the victim truck. Do not attempt to refuel the victim truck until you have repaired the fuel tanks. This may take a few trips, as the victim takes 300L of fuel and over 500 repair points plus 6 tires. This way, the truck will be able to move under its own power, which is necessary to get up some of the hills in question. This is not strictly necessary until you reach point of interest #2.

Additionally, you will need a heavy truck that performs well off-road. I used the International PayStar 5070, with support from an International LoadStar 1700. You do need a truck with good towing capability; the LoadStar was able to pull the victim truck some, but was not able to make it up the final hill.

Once the White Western Star is repaired and refueled, proceed along the route approximately as shown. The initial climb is not interesting until you reach the first left turn, POI #1 and #2:

1. There is a pair of rocks along the side of the road here, about 1 truck width apart. It is impassible while towing another truck.

2. There is a small lip at this point. In order to get over this, I had to tow the White Western Star backwards, so that the rear wheel drive of the White Western Star would engage on the other side of the lip, rather than being up in the air.

Congratulations, you're about halfway up. From here, things get a little tricky, but manageable if you know what you're doing.

3. There is a small valley filled with rocks in this region. Although it may kind of look enticing, and the closest way to the road, don't trust it. You will get stuck.

4. Proceed up the hill towards the power pole. This will get you away from the valley in #3. Once you're away from the valley, you can turn towards the road and start looking for an opening between the trees.

Congratulations, quest complete!

Just take it right up the hill by threatening accident mission way faster. The trick is you just need to repair the truck first so it will drive by itself when you winch to it, just like you want to do with most trucks you find. Don't bother dragging either, find a service trailer or make a couple of trips with a scout or pickup truck with repair parts on a roof rack and repair the vehicles you find then tow them with the winch.

repair it first then just pull it up the closests hill(north) to the main road, keep the winch line short. That way it will follow your driving line better, and make sure you stay on the road. did this in one try(when i tried it myself, when i tried it with my brother it went way different, but he was winching it). I think offroad truck is the best for this. last thing is don't follow the river path cut it short on the left-hand side where there are two smaller crossings.

After reading the other answers, I was sure it didn't have to be so complicated. It wasn't: did it one shot, shortest possible route.
I made two trips with a maintenance frame add-on on the Fleetstar to fully repair and refuel the WWS. Then, winched it along the same way as I came down from the 'Threatening Accident' quest-point, but before the boulders bottle-neck, I climbed the hill to the right, towards the copse of trees. Not a hard climb. Got stuck in two places, but all I had to do was let the winch go, winch myself up and pull the WWS again. It worked and I was right near the dam.

If you find a new vehicle all you gotta do is repair it and then get inside of it and recover to garage.