I just completed a trip from the bay area to kansas city and back without problems. Didn't run into any other Teslas at the superchargers east of Nevada other than at Denver. Many are in the parking lots of Holiday Inn Express hotels, which have coffee, warmth, and comfortable seating while waiting. I heard from the attendant at the Salina holiday inn that they had seen four charging before at once. I also saw a person several times starting in eastern nevada on the way back west doing the cross-country on a 60, which i thought was crazy, but they said that they were just careful.
The Topeka charger was very slow (~30kW) for some reason when we arrived into town, even being the only people there and trying 3 different posts. It was late so we decided to grab a hotel and charge in the morning, and in the morning we got about 95kW, so am not sure what was going on.
I did learn going there and back that the big hotel/casinos in Vegas have Tesla HPWCs. We stayed at the Bellagio on the way out and at Wynn on the way back, and both were happy to charge me up to full while I slept with no additional Valet charge... though the Bellagio did park the car out in their driveway with a bunch of other fancy cars for a while.
We also saw that the MountainHaus in Vail which is right on the highway has an HPWC as well, which would have also been a convenient place to stop with some more advanced planning (they were booked when we passed through).
I sure could've used a fast charger in KC, but we ended up cobbling together an adapter and an extension cord for my parent's 10-30 dryer plug and charged overnight with the window cracked.
Definitely the most comfortable cross-country drive I've taken.