How can I add my iPad to my Verizon service if it was not purchased from Verizon?

It gets worse. I bought my iPad Air with a T-Mobile SIM. It activated fine on T-Mobile. Then I took the Verizon SIM from my iPad 3 (cut to nano). The Air recognized the Verizon Network and asked me to sign into my account but would not activate. I called Verizon. The tech asked for the MEID, which is available in Settings/General/About. After some time trying different things he suggested, the bottom line is that as this was not a Verizon iPad, the MEID is not in its data base and they can't--or won't--add it. I verified this with a Verizon tech at a store and a second one by phhone.

Kicker: I inserted the SIM from my iPhone 5s (Verizon) and the iPad recognized it and worked perfectly on LTE. So clearly the iPad is capable of working on all networks, as Apple claims. Verizon is the bad guy here.

From what I understand, if one starts with a Verizon iPad Air it will work on all the other carriers with their SIMs.