I had a whole long post written out since you pretty much got on your knees and begged me to get on here lol. But then the battery died without warning on my lappy and I lost it all lmao. Oh well, here is the condensed version.
I would not replace the dampers with KBDD, they are just as hard as the ones you have now. If you are wanting softer, then go with teh stock v2 Pro Align dampers. But if your blade tracking is perfect, then this is not your issue.
Your heli is talking to you and you need to listen to what it has to say. I think you just answered your own question with your post above. You said "when under a load, the vibration quits". Your answer is in that statement. I will pause here so you have time to think about this....
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Did you get the answer yet? Well I have.
It's one of two things. Either it's the links have a lot of play in them, or there is something wrong with one of the servos. I would suggest putting in 3 new digital cyclic servos. I will almost guarantee this will fix your issue. the "load makes it stop" is your answer. If it was the gyro, then loading it up would more than likely make it worse. If you have to, put 3 mg90s servos in there or EXI D213F servos to test. However, because I have used then, and they work better than expected, the DS-410's are the way to go. They were rock solid on my Pro V2. Hope this helps.