I'd like to offer a few more details about this morning's journey to BG 40. How helpful these are, I am not sure, so keep in mind that YMMV, the writer is not an engineer, all warranties disclaimed, etc.
My Tracfone uses Android 7 and Verizon cell service. I took a bench on Sunset Blvd. when they moved the crowd rope somewhat further back from the restrooms, which was a little bit after 6:30 a.m. At about 6:52, I turned on cell data (no wifi, which I have found to work poorly at Disney parks), opened
MDE and scrolled down to the "Find Out More" button. Then I opened time.gov in Chrome and observed the time progress to about 6:59:55. After a few more seconds, I clicked Find Out More and Join Boarding Group and boom, BG 40. My sense was that Disney time was maybe one second later than U.S. government 'official' time, my main goal being not to be too early and get the 'sorry, we're not open' thing (or whatever the app does).
I also wanted to avoid anything involving refreshing, closing and re-opening, or any kind of back and forth with the app. My worry was that my relatively slow phone would not handle that well. The phone reported a pretty strong 4G LTE signal where I was, and of course it helped not to have a group to manage since it was just me.
And there you have it. Good luck to all future riders.