Update! LTE apparently works fine on T-Mobile in my area in southern Michigan! I just changed my max connection to LTE for my commute this morning and, though it shows I have no connection, emails were coming in. So, I fired up the Hardware Tests app and it said I was connected to T-Mobile's LTE. Then I did a speed test in Network Speed Test and got about 26Mbps down, but still no connection on data indicator. Called my wife to test voice and indicator changed to H+ on the call, but has gone back to no signal as I type this.
Moral of the story: don't trust the data indicator, at least not while on a different network!