Reposting these rotations from here
Target Synth: 2-Star - 2966 Quality, 233 Difficulty.
Needs 372 CP (with Comfort Zone) or 386 CP (Without Comfort Zone)
Cross Class Skills needed:
+ Byregot's Blessing (50 Carpenter)
+ Careful Synth 2 (50 Weaver)
+ Optional: Comfort Zone (50 Alchemist)
+ Steady Hands II (37 Culinarian)
+ Ingenuity (15 Blacksmith)
+ Manipulation (15 Goldsmith)
(Numbers in brackets below are for base quality gained per touch, assuming 340 Control)
1. Inner Quiet
2. Comfort Zone
3. Ingenuity
4. Steady Hand II
5. Basic Touch (+157)
6. Basic Touch (+183)
7. Basic Touch (+209)
8. Basic Touch (+235)
9. Basic Touch (+196)
10. Manipulation
11. Steady Hand II
12. Basic Touch (+216)
13. Basic Touch (+237)
14. Ingenuity
15. Great Strides [If excellent condition now, skip this step]
16. Byregot's Blessing (+1647)
17. Careful Synth 2
18. Careful Synth 2
19. Careful Synth 2
= 372 CP (for 3080 Quality Total, 114 above cap)
------------------------------------------------
Another possible rotation is below.
Identical cross-class ability requirements to the above rotation.
Stat requirements are 357 Craftsmanship, 343 Control and 348 CP (362 without Comfort Zone)
(This is +10 Craft, +3 Control, -24 CP compared to the above rotation).
+ Comfort Zone
+ Inner Quiet
+ Steady Hand II
+ Basic Touch
+ Basic Touch
+ Basic Touch
+ Basic Touch
+ Basic Touch
+ Manipulation
*** IF CONDITION IS EXCELLENT THEN USE CAREFUL SYNTHESIS II HERE ***
+ Steady Hand II
+ Basic Touch
+ Ingenuity (If condition is excellent, swap this and the next 'Basic touch' around)
+ Basic Touch
*** IF CONDITION IS NOT EXCELLENT THEN USE GREAT STRIDES ***
+ Byregot's Blessing
+ Careful Synthesis II
+ Careful Synthesis II
+ Careful Synthesis II (Only use if not already used for an Excellent Condition earlier)
(Note that technically it'd only need 343 control to ensure that it can weather a Poor condition on step #4 (the 1st "Basic Touch") - so you could attempt it with less control and just use your normal "Careful Synth 2" there instead if desired since it'd be incredibly unlikely to get 2 'Excellents' in exactly the wrong place...)
------------------------------------------------
You can get away with various Hasty Touch rotations if you just want to have a "really really good but not 100%" chance of a HQ.
And there are a lot of other "100% HQ with NQ materials" rotations out there, but these two are the lowest cost ones I've found so far in terms of Required Cross-Class abilities, CP and Control.