This is probably just bad luck but I wanted to ask before I threw away lots of money. The question is:

Is it possible for something other than crafting level and synthesis support to affect HQ tier rate? And maybe the break-synth skill-up threshold?

Since last week I've upped my crafting volume a bit, and particularly I have hit several unnaturally bad HQ runs. I noticed that the synth I was attempting today I was exactly 31 levels over both the main and sub crafts. Today my HQ rate was 5%, but normally I'm at the expected 20-30%. I'm wondering, for all the crazy crafting theories out there, if it's possible that something (day of week, moon, etc) can give an effective -1 to your crafting level which would push it from >30 to =30, changing the HQ tier from 2 to 1.

n=?

27 today, which is obviously low/inconclusive and why I'm asking others. Two other runs prior in the week were also around ~24. I don't have any recorded data. If it were theoretically true, not knowing the factors that cause the phenomenon would make it difficult to test since only so many synths can occur within a set period of time.

Lots of people have done actual extensive testing with recorded results and the basic consensus is that moon phase and day don't affect your results.
At 31 levels above the cap you SHOULD be getting a 25% HQ rate, like you said. But I've certainly gone 1/12 on T2 before and I've had runs where I've gone 7/12 on a T2...unfortunately there's more of the bad runs then the good it would seem.
Just today I did 9 synths that were T2 and of the 9 I got 6 NQ, 1 HQ and 2 complete breaks (lost all the mats). I know that's only 9 synths but I'm just trying to illustrate the randomness of crafting and Tier 2 in general.
Usually Tier 3 is consistent but I have actually gone 0/10 on T3 before...fun times.