From the sound of it you have to do something.
From what you've described his situational awareness and priorities may have slipped, and if that's the case, they have to be addressed. I can appreciate that you don't want to stir things up, but roles reversed, if a serious incident occured to you because you were stressed and no one had mentioned it to you, ask yourself how you would feel.
If an individual is stressed, they are generally not thinking clearly and may not be aware of their actions. I've been there. A good mate said I was pushing it, and I took corrective action. If no one had mentioned it, I would have thought everything was OK and carried on as normal. Until something happened.
All I can suggest is to post the letter. Don't make it a critical, damming, sarcastic note as ATCO's tend to favour, but try to word it in such a way as to show that you are concerned for safety as well as his well being. ATCO to ATCO as it were. You may find out that no one on the unit has had the nerve to confront him and you may just set the ball rolling; or the LCE's and managers may already be aware of the issue and can use your impartial opinion to back up their findings.
All a bit fluffy I know, but like I said, you can't really afford to do nothing.
