@OP; I feel like I'm sharing my dirty secrets by posting this; but here we go! And no, the people that tell youn that they can HQ things from NQ mats are not exaggerating

My rotation requires that you have multiple crafts levelled, it's kinda the trade off if you want easy HQ's from NQ mats:

Comfort Zone (50ALC)
Inner Quiet (All crafts around lv11)
Steady Hand II (Cul37)

[Progress Phase]
I'm one of those silly people that like to progress riiiight at the start, some people like to do it at the end and that's ok too. for my peace of mind, I get it done at the start.

Rapid Synth (Arm15) while Steady hands is up and stop progression until you're one Careful Synth II from completion (weaver 50).

[Quality Phase]
Use Hasty Touch (CUL15) while steady hand II is active, reapply steady hand II and comfort zone whenever you need to.
Use Tricks of the trade every time a good condition comes up.

If you're doing an 80 durability synth, use Master's Mend II when you hit 20 durability, or if you're on a 40 durability synth use Master's Mend I when you hit 10 durability left.

Keep buffing yourself with steady hand and comfort zone as needed.
Use Innovation (GSM50) if you can guarantee that the next 2/3 steps atleast will be used on hasty touch, really nice to use after a buffing cycle so you know you won't waste steps.
When you reach about 18% HQ chance use Great Strides (lv21, all classes) and then Byregot's Blessing. (If you have enough CP, use innovation again before these 2 moves).
This should put you at 100% chance for completion, even from NQ mats. As a warning Byregot CAN fail, to eliminate the fail make sure that steady hand II is up.

To finish the synth, one careful Synth II is all you need and BAM! HQ item!

As a warning, my rotation may not work for everyone; a lot of crafters have their own way of doing things and that's totally cool^^. I hope what I've written helps you in some way