Verizon SIM on band 2 & 4 in T-Mobile H811

Now that Verizon is rolling out band 2 and 4 LTE, I thought I'd try an experiment. Some background: I have a Nexus 7 LTE (2013) with Verizon data-only SIM, and an LG G4 H811 on T-Mobile. The H811 is SIM/network unlocked. I attempted putting the Verizon SIM in the T-Mobile phone. Full signal with Verizon SIM, but no "4G LTE" indicator. Attempted entering Verizon APN settings, but they would not save. (Is this device specific, or is the SIM card rejecting the APN settings?) Tried simply entering Name "Verizon" and APN "vzwinternet" but omitted MNC and MCC settings, and now "4G LTE" indicator DOES show, but no internet connection. Under About Phone/Network I am connected to Verizon on my H811 and Mobile network type is "LTE" but still not actually connected. Any suggestions for entering the Verizon APN info on a T-Mobile device and making it stick? I'm a paying customer on both networks, so please no indignant comments about "why don't you just ditch T-Mobile and/or Verizon?" This is just to satisfy my curiosity.

FYI, the Nexus 7 LTE (2013) does not have CDMA radios, so I don't care that the H811 also does not. Shouldn't the SIM work for the LTE bands that the H811 does have? Doesn't Verizon have some deal-with-the-devil arrangement with the FCC regarding their LTE that they have to allow any device on their network?