for something that has to be HQ (like the flawless weapon parts) i go all out on quality boosting. And wear as much control as possible

Byregot's Blessing
Heart and Soul
Magnum Opus
Purification
Greater Calling

I careful till rainbow then BB+MO > BB+Purification > BB+HS. if u get lucky u can get about 500 quality on those 3 synths alone. (if i dont get rainbow by the time i have 30ish dura left i just pop BB and HS or Pura and then hope one of the next two colors are rainbow. This can get up to about 400-500 qual in those 3 synths. when i hit 9 durabilitiy or lower i pop GC and if most of my carefuls werent 3% (careful gives 3-5% progress every time) you wlll be at 45-50% progress. when u pop GC u have 3 rapids to make up the final progress to finish the synth. each rapid gives 15-20% guaranteed with GC on. so if u have 45% to go ur golden. if u have anything in the upper 50s you might need to gamble on a 4th rapid to finish. most the time on high level synths i make it to like 45-50% so i have to get a few extra progress on my 3 GCs to finish.

This method relys on the 3 super boosted quality synths to make it worth while but since NQ results for class weapon parts are useless i think it works best