A couple of other thoughts,
1st I think there is a public RV park in Wicha Falls RV Park | Wichita Falls, TX - Official Website
I have not used it, as we have always ended up spending the night either east or west of there.
2nd be aware that when we were in Amarillo in October that I-40 was being widened going through town and a number of the exits were temporarily closed, there were also some rather large construction pavement humps in the road. This included the section of road in front of the Big Texan Steakhouse. I don't recall how long the construction zone was, but I would guess it was 3-4 miles or so going from memory.
p.s. just found this online, it looks like the construction zone is moving westward in Amarillo with sections of I-40 to be closed for the next several months https://www.newschannel10.com/2020/0...everal-months/