Like many others, I was having lots of problems with big team.
Monday I was having a great run of BTB games without any lobby problems (short of all my friends being on different fireteams than me) and here’s how (I think) we managed to avoid them:
- Add all your friends as mutual followers via their gamertag on the xbox website.
- Only invite them via the friends list in-game. Do not allow anyone to join via steam or in-game.
- Do not change your lobby’s privacy setting.
- Queue for BTB.
I was able to play with a group full of people on PC using both Steam and the MS Store version. We got over 5+ games in a row without any lobby problems.
I haven’t been able to verify that this works for this Tuesday/Wednesday, because every time I start the game I get 
NO INTERNET no matter what I do. (If anyone has any input for this I’d like to hear it.)
I figured I’d mention it in the off chance 343 manages to isolate the issue w/ joining via steam, unless the problem was solved by unannounced tinkering on their end.