Well for me as my skills have developed the subject has become less and less important and my interpretation and technique more. So for me the hierarchy would be interpretation/technique/subject. IOW I see something that interest me but I might not photograph it because the interpretation I have in my mind might not be possible. Sometimes technique might not allow me to get the image I have envision.
I think that your question is related to the search of your own style, and is a natural evolution IMO. I can only speak for myself, when I first started I wanted to take pictures like AA or Weston......so with that in mind I searched for the "right" subject, then I applied all my zone knowledge (interpretation) and then I would go to the darkroom and try to get the "perfect" print (technique). As my skills evolved I see less and less this rigid process, I have not done film testing in many years, if I try a new developer I just measure the shadow densities and adjust EI, but testing developing, N+, N. N-...forget it! Of course when I first started I tested every film and developer combination under the sun...I had great charts, notes, H&D curves...but not a single good pic. It was not until I made a good print totally different from what I had envisioned that I realized that technique allowed me to get a good print out of a bad neg, and that my interpretation was not chained to the subject but was a product of my imagination and what I "saw" in the negative.
I beleive that if I am to endow the print with some kind of "feeling" I must depart from reality, and in a sense we all do when we apply filters, N+ or N- developing etc, we are taking the image away from what is really there and adjusting it to our desires.
So I will post the image that changed my opinion, merely to illustrate my point, the negative was flat, the contrast was not there and the straight print was just boring......with a little bit of work and experimenting a descent print came out, and as a matter of fact was my first sale.