Two locations in Why, AZ - one is the Why Not Travel Store right at the intersection of AZ-86 & AZ-85. The *other* location is about a mile to the east along AZ-86, the casino there just inside the reservation border (that's where I got mine...) has fuel available 24 hours.
Now, I didn't do the NC version, but the MS version. I thought the ride info said Seagrove was the alternate location for Whynot, NC. Apparently, in doing research (another one of those 'future rides for consideration', a couple of years ago), a lot of pottery places in the area, but might be difficult to time a ride to get a receipt at one of those locations.
@SteveAikens mentioned the long ride out to Why, AZ to begin a ride. I took some lessons from that and spent the night in Ajo, AZ for the first (and only) time I've done it. Think the next time, I might consider Gila Bend instead.