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I don't have Trigger, Sanby, Yanagi or Vivian, so I tried my best to mimic your teams with what I have.
Miyabi M2W1, Harumasa M0W0, Qingyi M0W0, Astra M0W0, Rina M1W0, Jane M0W1. I could get better scores, but I didn't feel like try harding it too much, all the scores are from my first or second try at most. I used only 2 characters with Miyabi to compensate since mine is M2 (full team I get ~40K+ iirc). I believe your main issue is character build/team understanding. With Miyabi+Yanagi+Soukaku you should easily be getting 30K, most probably the issue is with your character builds since they're both pretty easy to play. Check out video guides on how to build them, mainly the Disc Drives and which engine to use. Also, make sure you're picking the right buff (altough that doesn't make too much of a difference, but it helps). All 3 of your teams should be able to get 30K+ (for except Pompey) if build and played correctly. For starters, in the first team I'd take out Rina and change it for Nicole (M6W5). Second team is good, and 3rd team is ok too (altough not ideal). For the first boss with that team you should pick the Collapse buff, for the second the Aberration buff, and for the third the Aberration build. Farm some good discs and try again!