TS2000 is suggested to use for CAT. I have been unsuccessful with it so far.
Each mode has its own filter width with 4 choices each mode, and mode specific it changes from mode to mode. Digital mode seems unfiltered but this allows sliding up and down the waterfall, those other signals are not filtered out.
Not sure about the QST SWR problem. I had to return twice, but the third LD-11 came back working quite well. I have a tuned EndFedz Quad which has no problem whatsoever with SWR on those four bands. The rig will power down output as SWR rises.
VOX is adjustable for SSB and separately for CW (must be on for CW to work with paddle). there is a separate phono jack for PTT.
The hand mic is rugged and does use a side button for PTT. Also, there is VOX.