Hi there--just got back from a lovely trip, and this thread was a big help when planning, so I figured I'd share our experience.
We tried for a BG the morning of 5/23 (I believe HS had increased capacity by this point, compared to earlier in the month). We were saying at Riviera, and for some reason our room location had horrendous cell reception, so we went down to the central courtyard area at 6:45 am to do it there (was around three bars instead of one).
The plan was for my husband to try wifi while I used data, but apparently he forgot to click through to confirm connection to Disney's wifi... so it turns out we both were just using cell data. We made sure all other apps were closed, bluetooth was off (and in my case wifi was totally off as well), and we restarted and re-logged into
MDE (both phones on my account) about 30 minutes in advance.
We used the "refresh-join-join" method, where we started by clicking through from the home screen (the AT-AT pic) in advance and then just refreshing that page periodically by pulling down on the screen. We didn't have an external countdown clock, but we checked our phone clocks in advance and they were within a second or so of time.gov's clock. Then after 6:59, I just did a rough verbal countdown so we knew approximately when the time was going to roll over to 7:00. My strategy was more of a "wait until the clock hits 7:00 and then immediately refresh" while my husband just started constantly refreshing when there was 20 or so seconds to go.
So, the results... I honestly don't know if my own strategy would have worked, because when 7:00 rolled around, I refreshed, hit the "join" button, and started freaking out because I didn't see our friends and family list or another join button... just an "error" screen! Turns out the "error" was that I was already in a BG because my husband had gotten through first, lol. He told me he had just constantly refreshed starting prior to 7:00, and as soon as he saw the "join" button he clicked through everything else ASAP. He must have had perfect luck with his refresh timing, because we were literally in
BG #1.

I was so stunned I took a screenshot. Needless to say, we were both elated, because we honestly didn't expect to have much of a chance for a BG (especially on our first try).
Anyway, the ride was great, and as far as I can tell it seemed like all of the noticeable effects and such were working.