Way back I rode from Cherry Hill to Wildwood a few times, Maybe not 100 miles but pretty close. That was on a bike I've owned since new, a Panasonic sport 1000. Still ride this bike often but lucky if I ride 20 miles a day.
Here is one local to me that doesn't look to be messed with. https://southjersey.craigslist.org/bik/d/toms-river-26-schwinn-beach-cruiser/6908315104.html Interesting about the HL stem, I have an 89 with the same stem and fork have to open it up and look at it.
That's not a serrated nut on the drive side. That's the sun gear, the lock/jam nut is in the center of it. Shouldn't have any play. You really need that tool or to make one if you want to adjust it proper.
I'm gonna say the sellers are just as bad. If you are lucky 1 in 7 will answer there ad. After a week of trying to reach them I send them a "can you take down your fake ad". Sometimes you will get an answer like, oh it sold but I don't know how to take it down or I was on vacation and didn't...