Performed the tests Fabrice suggested below, basically cleaning, inspecting measuring fibers and sleeves at the HAM6 green fiber feed-through, with no improvement.

1 - Couple a new low insertion loss fiber (let's call it 'Air-3') after the the current one ('Air-2'), and check the transmission.
2 - Remove the mating sleeve at the feedthru,  gently clean the tip of the of the feedthru ferule. Spray air in the mating sleeve and put it back on.
3 - Connect 'Air-3' to the feethru, and check the transmission.
4-  Remove 'Air-3' from the chain

Initial power 20.4mW at input coupler -> 2.6mW out on green Refl.
Take out 'Air-2' inspect, -> transmission=12.5 mW. 'Air-2' looked scratched replaced with 'Air-2_5'  transmission 12.6 mW (end A/B insertion loss .41/ .45 dB)

'Air-3' (end A/B insertion loss = .10/.15 dB). Power trans 'Air-3' = 10.5 mW. Remove mating sleeve at feed-through, clean feed-through ferrule, spray mating sleeve replace. Insert 'Air-3' transmission on green Refl = 0.5 mW

Remove 'Air-3', clean 'Air-2_5' again insert -> 1.5 mW onto green Refl.

Put original 'Air-2' back -> 2.6 mW on green refl.

This is now the max. I could not recover any more power regardless of how "loose" or "tight" the connection was. It's possible the ferrule may have been scratched or got contaminated when putting the sleeve back on (it's rather awkward). The ferrule can be cleaned but not inspected because of the location. After the 1.5mW transmission measurement with Air-2_5'  I was just glad to recover 2.6 mW transmission with 'Air-2' to green Refl, which after Nutsinee's latest post, still allows us to move on for a bit.

Note 'Air-2' had very low insertion loss at the HAM6 end (.15 dB) and this is probably why the transmission to the vacuum fiber was better than 'Air-2_5' even though 'Air-2' was scratched.