15% is 'half' in FF14 crafting so if you can get 15% you can pretty much 100% with HQ mats.
The problem is, I don't know if you are high enough level and gear, a Muscle Memory might complete the Synth.
If not,
Muscle Memory
Inner Quiet,
waste Not
Basic touch x 4
Masters Mend
Basic touch x2
Great Strides, Byregot's Blessing
Careful Synth

I doubt you will make it to the BB if you are using all HQ mats.