3 inch quad shaking - too sensitive flight controller?

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I recently built a Eachine Tyro79 3-inch quad and the drone vibrated under throttle on 3s and stock tune. It flew alright once I had adjusted to very low PIDs, but since upgrading some parts, I can't seem to get it flying smoothly at all. I changed to Diatone Mamba Toka 1606 3100kv motors, a Foxeer Razer, and 4s 850mah batteries. During initial test flight with these upgrades, the drone would shake and wobble through corners and backflip and crash into the ground in a sharp turn. I've upgraded to betaflight 4.3.1 with rpm filtering and followed Chris Rosser's filter tuning and PID tuning YouTube videos, but it still isn't flying well. The flight controller has been soft mounted as a part of this kit since the build. I've tried dropping the PIDs all the way down to P-20 I-10 and D-20 and it still shakes. The motors aren't more warm after a flight but I think the last possible option is that the FC is just too sensitive, unless the frame has a very strong resonance. Is there anything else I should try? Do I just need to buy a new FC?