How can stress (and resulting tight shoulders/neck) make mild to moderate cervical stenosis worse? any tips for relief?

Stress does not per se make stenosis worse, you just feel more pain because the muscles are tensing up . A muscle relaxer like Baclofen or cyclobenzaprine may help but you can not drive as they are sedating. Motrin like products can control the inflammatory pathway that causes pain.

In addition to Dr. Glicksman's answer, would suggest you handle this more aggressively, using physical therapy and eventual McKenzie neck exercises as tolerated. Meditation and/ or acupuncture could provide relief as needed.