I got the update (VRUDMI1) this morning in metro Atlanta. I want to say a word about the process, in case others also run into issues.
The notification screen had a link to a Verizon support page with a bit of information about what would be updated (nothing about "eSE Removal"). That page had a link to detailed update instructions, but trying to actual download that PDF failed on several attempts. Your basic Verizonism.
So then I tapped Install update on the update notification screen. The phone restarted, and that's when the real issue occurred. I got an alarming and confusing screen with some tiny blue text and a kind of broken Android image on it. Looking closely and squinting (I should have used my camera to take a picture!), I made out something about "Manual mode," followed by a series of options that included Restart system, Update from ADB, and various other inscrutable update options. I chose Restart, fortunately. The restart was normal, and ended with a notification that the update had been unsuccessful, and an offer to try again. Plucking up my courage, I tried again. This time it began by downloading the update, with a typical download progress bar in the notifications. I think that must have been the problem in the first place: it tried to install the update before downloading it.
Once the update was actually on board, the install proceeded smoothly. During the automatic restart after the installation of the update, there was a process in which apps were converted or conformed or something. That also went smoothly, and everything seems to be OK.
So, the moral of my tale: If you get the update notice, see if there's a way to make sure it downloads before you accept the installation. If you get that alarming text screen, select Restart.