Looking over your rate tuning I'd like to suggest a different method of making the settings for roll and pitch. First set the low-pass filters back to at least 10Hz. You have them set at 4 Hz. Suggested would be 10 on pitch, 12 on roll.
Now set the rate P, I, D gains all to zero for both pitch and roll. Set the rate VFF for both pitch and roll to a level that looks like it provides normal swash response on the ground. Suggest starting with 0.15 for both. Test fly the helicopter, fly it in some figure 8's, make some fairly quick roll and pitch inputs on the cyclic, etc. Do this only in Stabilize flight mode.
Note: if you get any pitch bobbing with the above settings you have a mechanical problem with the heli - either blades not tracking, blades out of balance, or CG issue. Fix it before proceeding.
Pull the logs from it and look at the Rate in the logs and see how desired rate matches actual rate for pitch and roll. If it doesn't track desired vs actual rate control, turn up the VFF until the graph lines show the two tracking each other. If the helicopter gets too responsive, then adjust these values down:
Experience says you'll end up somewhere around 80000 to 85000 for a 550 on those settings. And VFF of .15 to .20, depending on the mechanical rate of your servo linkages and servo speed.
After you get a nice flying heli with the above, tune the PID's one axis at at time. I suggest starting with roll because it is normally the more sensitive axis. Leaving P and I at zero, set the rate D gain to .003 and do a brief test hover a few inches off the ground. Increase the D by .001 at a time until you get a side to side shake. At whatever value you get the shake at, cut it in half and enter that as the final value for D gain. Enter the same value for pitch D gain.
Do the same thing with rate P gain, except start with .05 and raise it .01 at a time until you get the side to side shake. At the value where you get the shake, cut it in half and enter that as the final P gain value, enter the same value for pitch.
For I gain set it to the same value you used for the VFF for both pitch and roll. Ex: if you ended up at VFF .18 on roll and .20 on pitch, set the rate I for roll to .18 and pitch to .20.
Now, test fly the helicopter again just like you did in your video and see if the problem is gone.
Just for reference sake, and it is unlikely your tuning results will be the same, this is the values I use with a Trex 500 with a DDFP tail mod, stretched to a 550, swinging Rail 516's at 1,850 rpm with a DFC head.
ATC_ACCEL_P_MAX , 86000.000000
ATC_ACCEL_R_MAX , 110000.000000
ATC_ACCEL_Y_MAX , 27000.000000
ATC_RAT_PIT_D , 0.003000
ATC_RAT_PIT_FILT , 10.000000
ATC_RAT_PIT_I , 0.200000
ATC_RAT_PIT_ILMI , 0.000000
ATC_RAT_PIT_IMAX , 0.440000
ATC_RAT_PIT_P , 0.090000
ATC_RAT_PIT_VFF , 0.200000
ATC_RAT_RLL_D , 0.002500
ATC_RAT_RLL_FILT , 12.000000
ATC_RAT_RLL_I , 0.180000
ATC_RAT_RLL_ILMI , 0.000000
ATC_RAT_RLL_IMAX , 0.440000
ATC_RAT_RLL_P , 0.080000
ATC_RAT_RLL_VFF , 0.180000