Yes I believe your on the right track. Tune pids till its smooth most of the time. Half throttle and below. Then Add TPA, which reduces the PID's at higher throttle to get rid of thoes high throttle shakes. Usual TPA activation point is around 1500 on the throttle, so about half. Example. TPA start at 1550 at 10% reduction in PID and at 1900 have it like 50% reduction and see how that flies. (If that makes sense) you may only need 20-30% reduction in PID at full throttle. So play with it. I've heard of some guys using TPA to increase PIDs like 10% at low throttle for flips and acro flying at low motor rpm. I'm not exactly expirenced in setting up TPA, but I believe you are on the right track. Look on google or the LP wiki for TPA examples if you get confused.
What does it do if you lower your P for pitch and roll below the 210 mark. Try like. .00190 for pitch and .00175-.00180 roll. With your quad being longer than wider(the body) it's will need a slightly higher pitch p gain than on roll. Lower your I a touch too. Come down .00020-.00030 on I with the gains too. Like 620 for roll and 630-640 for pitch. It looks like it fkys just fine except the shaking. To high P can cause the the high frequency occilating. Are these default PIDs?
If you like the way it flies control wise maybe just fiddle with the TPA first.