It seems I am almost in your exact position, except that I have Frontier. 3v3 games are no problem, but on 6s I get kicked after a few minutes. Oddly, I often can't rejoin friends in the game because I am replaced immediately. I have done dozens of line quality tests and found nothing amiss...no packet loss (which is the supposed cause of "Bee"). No other games have ever given me trouble, leading me to believe that the connection to Destiny servers is uniquely "fragile."
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Same here. Frontier also. Had a tech out here this morning to double check everything. Exactly as you described.