Right ppl. got the game running in the end.
Doing that file integrity check fixed the problem. Even though it went from 34 to 33 "bad" files and refused to go lower, that one fix seems to have done it.
For some reason, voice quality is that of a poor mobile phone when it should be hi-fi, though.
That player must be removed issue was, ahem, user error. It was the free-for-all game multiplayer mode where you can't be in a party with anyone since everyone's out to kill each other. Such fun! Selecting one of the other modes worked fine. The game is demanding on this old hardware though! Hard to keep up a decent framerate in some maps. Others are sorta reasonable, even though my RTX 2080 SUPER is hardly top end and a 4 year old GPU design, it's still not much of a bottleneck, it's my ancient 2700K from 2011 that desperately needs upgrading. Gonna miss this old workhorse when I eventually do.