Your description sounds almost like the Dempster Highway with Eagle Plains Motel being halfway point and Fort McPherson being the village. I had my challenges on the Dempster Highway. It wasn't a mechanical issue as much as weather. It rained and snowed on me (in July) as I was getting closer to Fort McPherson about 20km away. This particular part of the road was worse quality gravel and became a slippery muddy mess. Two trucks came by and offered me a ride but I was too proud (or stupid) to accept. However, by time the third truck offered, I accepted and rode last little bit in the truck.

As far as some stranger things that have happened on tours:
- I was cycling the Natchez Trace when my pedal snapped off. It was Saturday afternoon and I rode with one pedal the remaining 20 miles to Houston, MS. There is no bike store in Houston, but there is a Walmart. Unfortunately, Walmart pedals were 1/2" instead of the 9/16" I needed. So I kept looking and eventually found that a spark plug had same threads. So I cycled next two days until I got to Jackson, MS with a spark plug instead of right pedal.
- I led a trip to Cape Cod while in college and we were out enjoying a day ride in Nantucket Island. One cyclist from our group was enjoying beautiful scenery and not paying enough attention to ride smack into a parked car. Metal rims and metal frame damaged and looked like it would be the bus for her. However, when we walked to the hostel, turned out a gentleman on vacation from NYC heard of the plight from others in our group. He donated his bike for my friend to be able to continue. We asked multiple times but he was serious and it was much appreciated.
- Cycling across Russia with tour partner. We got separated leaving city of Kazan. Somehow didn't find each other except for somehow picking the same hotel in Ekaterinburg 10 days later.
- On a cycle trip - but not while cycling. Finished trip in Chennai and went to hotel to arrange an (guided auto tour) of the city. The guide wisked me past many of the interesting sites in my guidebook, barely stopping for some of them. However, he then had multiple hours left before he was supposed to bring me back to the hotel. So he first took me past a few expensive rug shops. As that struck out, he instead took me home. I met his family, saw where he lived and was shown off to the neighbors. Invited me to participate in local festival, though just as festival was starting, time was up so drove me back to the motel. Getting a sense of local living was far more interesting than those guide book highlights would have been.