When moving across country when we had our 5ver, I tried to plan stops but sometimes that just doesn't work out. I'd Wally World it from time to time, but never unhooked or put the gear down. One time forgetting to put it back up and the trip is delayed or ruined. Didn't need to put the slides out, but it looks like your needs are different. I would never put my slides out in a rest area if I had to be in with the trucks. Good way to loose a slide. Many Flying J's have an RV-only area.
We just did a round-trip from NW Ohio to Grand Canyon. If you're going to take 57 out of Effingham IL, 12 miles after you cross the Mississippi at Cairo is Sikeston MO. Eat at Lamberts in Sikeston, you can Google it for particulars. Quite an experience. Large lot on the east side of the building for your 5ver. Also, a good place to stop for the night if you're taking 160 across Colorado is the Lathrop SP just west of I-25. Mainly pull-thrus, electric on site, water nearby, good clean showers, easy after hours check-in. Gives you a full day to cross the Rockies the next day and get you to Durango where there are a ton of campgrounds. Some may be closed for the winter already. Weather across the Rockies is a concern this late in the season, so maybe you're going I-40 instead.