An update on my exploratory trip...
My travel path took from Kansas City (northeast corner of Kansas), almost straight south through eastern Kansas to just shy of the Oklahoma border, and then west to Wichita in south kind-of-central Kansas, 150-200 miles per leg.. The route was on secondary highways-- no interstates around. To give an idea of population density, many of the towns are big enough for a Dollar General store, and way too small for McDonalds.
tom67's suggestion of Network Cell Info Lite worked great for my application! I could leave the app display on, and snooze the screen between peeks to limit screen battery drain. A couple of swipes let me see what coverage was like, and the connected band (if any....).
T-mobile's coverage in the area was... well, interesting, but far from great. The last time I'd tested, this was a large black hole for T-Mobile, and for Sprint.
My test phone was a factory-unlocked Moto E6 with a Tello GSM SIM. I did have tower connections on a large percentage of the route, but signal strength so low that I either couldn't place a call, or couldn't sustain a 2-minute call. Complete loss of tower connection was frequent, and dropping to GPRS/Edge/2G wasn't unusual.
I mostly saw Band 2.
Band 66 is one small area-- not sure why that appeared, since I thought band 66 was primarily used to relieve data congestion in busy areas.
Band 71 popped up once or twice, but with no improvements in call capability over the Band 2 I usually saw. (I know Band 71 travels further, but I must have been on the edge of whatever 'further' is....).
I was intrigued that near one of the larger towns (10,000 population), I saw Band 41 now identified as T-Mobile. It was usable if not strong, maybe 20 miles outside Wichita. I'd guess that repurposing that band let T-Mobile expand their Wichita coverage footprint. (Wichita itself has fine T-Mobile and legacy-Sprint coverage.)
Watching the bands and signal strength was interesting. I find it curious that T-Mobile 'technically' has coverage in a lot of areas that it didn't have at all the last time I tried, but that almost none of the technical coverage was actually usable coverage. It's still a black hole, other than allowing T-Mobile to color some areas of the map magenta..