First off, regarding the "blank year" in between the Asylum escape and Hong Kong: the mission briefing from the ICA states twice that the Kowloon mission is your first. Therefore I do not think Beld. Manor or Meat King took place during this time.
At the beginning of SA, we see the two guys (forgot their names) go to the Asylum and find the bodies of the staff/patients. Unless those bodies decay at an extremely slow rate, I think that the intro of SA took place close to the end of C:47. If you believe this, then that means there was a lengthy amount of time between the intro cutscene of SA and the cutscene of 47 in the garden in Sicily (because Asylum Aftermath mission happened in 2000). Could Beld. Manor and Meat King happen in this time period? Maybe, but it doesn't make much sense to me. What would be the reason for 47 to turn to religion if he hadn't stopped at the end of C:47? I think the killing of his creator -- and, hence, a want to believe in a new creator -- is a better catalyst for change than abruptly deciding to put away his guns for a quiet life.
I think we can all agree that SA occurred in its entirety without being interrupted.
What's left is the time in between SA and BM. To me, this is the most probable time for 47 to do Beld. Manor and Meat King because we know 47 went back to contract work. We also know that in the briefing of Meat King, Diana says "it's good to work with you again". Perhaps this is referring to 47's decision to return to steady contract work? Again, maybe. I don't have any concrete evidence to back this up...it's just a feeling. Ultimately, until someone from IO clears this up, we can only have theories.