Here's my experiences with Shihei.
With alchemy 60, and wood 68, I can make more money making the ingredients for shihei, than shihei itself.
I only make it for myself, and a few members of my LS, it's time consuming to do it the cheap way.
You will need, at the very least, Alchemy to 55, and Wood to 60
with Alchemy 55, you can HQ Black Ink very easily, about 50% HQ rate, depending on the day.
Dark Crystal + Nebimonite + Distilled Water + Windurstian Tea Leavesx2
You can't HQ Bast Parchment, but it's still cheaper to make. Elm Logs are ~8k each, but bast parchment sells for 11-12k/stack.
Lightning + Elm Log + Distilled Water + Moko Grass
With wood at 60, you can HQ Shihei at about a 25% rate, depending on day. Sometimes I HQ 1/12, sometimes 6/12.
Take wood to 80, and you hit the 50% HQ tier, but I wouldn't recommend this, unless you plan on taking wood to 100
Wind + Black Ink + Bast Parchmentx2
The easiest way to do it:
Make Bast Parchment on Lightningsday. It's not HQable, and you don't want to be blowing up elm logs.
Make Black Ink on Lightsday, should provide the most potential for HQ
Make Shihei on Darksday. You could wait until Iceday, for about the same HQ rate, but I seem to get more breaks on iceday than darksday.
These 3 days follow each other, so plan ahead, and get synthing.