I hear you, Kor of Memory. My war party includes a player who suffers all the same afflictions you do (as well as not being able to join fireteam half the time in social spaces - even with player slots available). He plays Xbox One. I'm not sure what speeds you're running, but my friends ATT internet is quite slow, and strictly wifi, which exacerbates the testing issue.
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I've got att inverse but it's high speed fiber. Both of our consoles are also wired.