Thanks to everyone's suggestions, we were able to get BG 6 on Mon., June 22. In addition to everything everyone has suggested, what helped us the most is:
1.) at 6:50 a.m. we went outside and walked around until our phones had 4-5 bars of data. The data speed-checks for Wifi vs. Data we did inside (AoA, Cars, Bldg. 2) were inconsistent, but when we walked outside, our data bars were consistently full.
2.) Instead of swiping down to refresh the Join screen, we clicked on the golden Theater icon. For all four of our phones (two iPhones, two Android phones; Android was the winner), clicking on the icon was significantly faster at refreshing the screen than swiping.
Btw, all of our names were pre-selected and location was turned off. We were each logged on to our separate
MDE accounts (all linked as Family & Friends). We were given from park opening until 9:40 a.m. to ride.