Well, bypassed Vroom and went straight to the company they have handle the registrations. The guy wasn't supposed to deal with me directly, but once he heard my tale of woe, he took care of things.
Vroom basically lied to me, and had taken no action with the revised paperwork required. They told me on multiple occasions that paperwork had been sent on 12/17 and I should receive my registration by the end of the year. That was not true, and nobody was doing anything to move this forward.
I got the Jeep registered Monday and inspected yesterday. And to add a little humor to this, after the temp tag expired back on 12/20, I just received FedEx notification that a new TX temp tag from Vroom will be delivered today. Thanks guys.