Must have abilities for this method
Cooking lv15: Hasty Touch (100% progress, 50% chance of succes, 0cp)
Cooking lv37: Steady Hand 2 (this is easily one of the best, but it's a lot works to unlock)
Alchemy lv15: Trick of Trade (give you 20CP on a good, no cost)
Goldsmithing lv15: Manipulation (10durability every turn/3 turns)
Carpenter lv15: Rumination (Give you back CP for every stack, up to 60).
For rumination, the amount/stack restored was posted by stevenl4 in this thread)
Highly recommended
Blacksmithing lv15: Ingenuity (lower the synth level to your current level)
Armorer lv15: Rapid Synthesis (250% progress, 50% chance of success)
Leather Craft lv15: Waste Not (Cut the durability cost by half for 4 turn)
I didn't include the lv 50 abilities, because they are a pain to obtain, and you don't need them to HQ reliably, but most of them are worth getting (except armorer).
Quality Phase gambit
#1 Inner Quiet
#2 If there is a "Good" rating --> Trick of Trade
#3 If there is "Excellent rating" --> Advanced Touch
#4 If Durability is at 20/40, 10/70, or 20/80, use Manipulation or Master Mend II (Manipulation for
40 synth, Master Mend II for 70/80 synth)
#5 Steady Hand 2 (SH1 until then), and reapplies every 5 turns
#6 Hasty Hand spam
If, and only if you have plenty of IQ stacks, and got some CP that is about to be wasted, feel free to blow them on a "Good" rating for the large quality boosts
In fewer words, we could simplify it to Inner Quiet > Steady Hand > Hasty touch, with Trick of Trade on every "Good" rating. That's essentially what it come down to.