After searching for a rotation with high HQ success with NQ mats for my particular stats, I have one that has been very good so far. A lot of the rotations I have seen require more CP than I have so for those with a bit less this has worked for me very well. (This rotation was actually given to me by Cerak in my FC so the credit goes to him.)
Stats:
372 Crafting
361 Control
344 CP--> using regular stone soup(vendor) +17 CP for a total of 361 CP
Using Hasty Touch means at the mercy of the RNG which means some synths will be terrible on fails so this is not a guaranteed 100% but I have had very high success with it. (If I had to guess maybe 90-95% HQ results starting from NQ mats)
1. Comfort Zone
*hit Tricks of the Trade if good condition
2. Inner Quiet
*hit Tricks of the Trade if good condition
3. Steady Hand II
*hit Tricks of the Trade if good condition
**hitting Tricks here will result in only 3 Hasty Touches after the next Manipulation
4. Manipulation
*NOTE: for every Tricks hit above you can substitute a Basic Touch for one of the next Hasty Touches to eliminate the RNG (I wait for good conditions when substituting my Basic Touch(es) in. You can wait until the next set of touches as along as you keep track of your substitute chances.)
5. Hasty Touch
6. Hasty Touch
7. Hasty Touch
8. Hasty Touch*(see step 3 notes)
*hit Tricks after the last Touch here if good condition pops, see NOTE above
9. Steady Hand II*(same notes as step 3 above)
10. Manipulation
11. Hasty Touch
12. Hasty Touch
13. Hasty Touch
14. Hasty Touch*(see step 3 notes)
*NOTE: at this point you need a minimum of 131 CP to finish this rotation
15. Steady Hand II
16. Great Strides
17. Innovation
*hit Byregot's here if good condition pops after Innovation
18. Ingenuity II
19. Byregot's Blessing
20. Careful Synthesis II
Simulator link: http://link.ffxivcrafter.com/?id=cbf5k