Persistent tooth pain after two root canals - same pain for 10 years. Upper left molar (#14)

I've (32M) been dealing with a persistent tooth problem for over 10 years, and I need professional insight. Here's my situation:

• Upper left first molar (#14) has had root canal treatment twice
• The pain hasn't changed much before, between, or after both root canals
• The last root canal was done just over a year ago, and I'm certain nothing has changed - the same pain persists
• Pain characteristics:
  • Dull, irritating pain that radiates vertically up into the cheek
  • Feels somewhat like numbness
  • Pain is periodic (some weeks worse than others)
  • The tooth specifically reacts to forceful touch/movement (if I try to wiggle it), while adjacent teeth have no reaction to the same pressure
  • Pain seems to worsen when my immune system is down (even with minor colds)
  • Cold sensitivity test confirmed the tooth is non-vital (dead), yet I still feel a dull response to cold foods - not the sharp, shooting pain typical for live teeth, but definitely noticeable

Medical history:
- Seen at least 5 different dentists, including two specialists who performed the root canals
- After first root canal, experienced severe pain for 2 weeks (had to take sick leave)
- Had 6 other root canals done with no similar issues
- Adjacent teeth: #13 has an old root canal (no issues), #15 is completely healthy
- Multiple detailed X-rays and scans show nothing unusual
- Sinuses are healthy and clear
- Non-smoker, non-drinker

The last endodontist claimed it's impossible for this tooth to have any sensation and suggested the pain must be referred from adjacent teeth. I strongly disagree based on the specific pain location and symptoms.

I'm considering extraction as a last resort. Has anyone experienced something similar or can offer any insights? I'm tired of relying on ibuprofen for the past decade. While the pain isn't severe, it's constant, troublesome, and extremely exhausting to deal with.