Ah, you're really up to something here!
As we can see of the Stardaters, the events in
Rascals takes place at Stardate 46235.7 (Friday, 28 March 2369).
Then comes the events in A Fistful Of Datas at Stardate 46271.5 (Thursday 10 Apr 2369), the events in
The Quality Of Life which takes place at Stardate 46307.2, (Wednesday 23 April 2369 ) and the events in
Chain Of Command which takes place between Stardate 46357.4 (Sunday, 11 May 2369) and Stardate 46360.8 (Monday, 12 May 2369). I assume that those official Stardates counts for the days when Picard was hold prisoner and tortured by Gul Mardred,
Then O'Brien is transferred to Deep Space Nine at Stardate 46379.1 (Monday 19 May 2369) in the SD9 episode
Emissary.
As we can see, O'Brien is not visible during the events between Stardate 46235.7 (Friday 28 March 2369 and Stardate 46379.1 (Monday 19 May 2369) when he all of a sudden shows up on Enterprise to say goodbye to Captain Picard.
It's about one and a half month!
So what did actually happen between those weeks?
Was Picard so annoyed with O'Briens performance during
Rascals that he actually demoted him? Was O'Brien court-martialed and sent to prison? And were the friendly scenes between Picard and O'Brien in
Emissary the result of Picard getting second thoughts of his treatment of O'Brien, got him released from prison and re-instated in Starfleet again-but with a lower rank and O'Brien being grateful for that?
Or was it still about O'Brien spiking Picards tea with Irish Whiskey so that Picard got drunk an made a fool of himself during a reception for some Admiral on Enterprise?
Or was Keiko involved?
KEIKO O'BRIEN: I can't stand another day in this stupid tin can of a ship. I wan't you to be re-assigned to some base on a planet where there are sunshine, gardens, flowers, trees and a blue sky.
MILES O'BRIEN: I'll talk to Picard and see what I can do.
Some weeks later:
MILES O'BRIEN: I've fixed it. I will be transformed to the Bajoran sector in about two weeks.
KEIKO O'BRIEN: Great! I knew that you would come up with something! I've heard that Bajor is such a wonderful world, the whole planet is like a garden and....
MILES O'BRIEN: There's just one problem?
KEIKO O'BRIEN: (Angry) Now
what
?
MILES O'BRIEN: We're gonna live at a space station above the planet called Deep Space Nine. And I've been demoted. Picard became angry as hell when I wanted to be transferred. He called me an ungrateful SOB who have thown away my chances in Starfleet and messed up my carreer.
KEIKO O'BRIEN: Oh Miles.........
So there's still a mystery to solve.
As for O'Briens yearly round of torture, I don't think that Picard have as much influence that he can persuade the T'Lani, the Kellerun, the Parada and the Cardassians (well he might have got in touch with Gul Mardred after rerlationships between the Federation and cardassia got more friendly) to order a recurring torture of O'Brien. I must have more to do with some ancielt curse or so.
Maybe something for further investigations as well?