As I said earlier, my 5.56mm No4 project only got as far as firing and extracting with a 7.62mm extractor. It extracted well enough in spite of the thicker rim of the 7.62mm over the 5.56 rim but didn't proceed to to ejecting. While on the subject of rim thickness, the extractor certainly clawed the 5.56mm rim during the primary extraction phase. ON that basis, the primary extraction operated perfectly too.
However, I did get a 9mm to extract and eject (except the the last round wouldn't eject successfully) using the left body side friction to cause ejection. What I did was modify the underside of the 7.62mm extractor so that the claw moved over the bolt face to the left more so that the repositioned tip of the claw would physically push the smaller 9mm case (but same base rim diameter as the 5.56mm case) further over to the left hand body side wall to effect ejection. This worked well and in theory SHOULD work for a 5.56mm case. I didn't do anything about the extractor spring tension.
I don't think that eccentricity of striker played any part in my feeble efforts and certainly didn't suffer with any misfires as a result of it.
Just from the 'keep it simple' engineering point of view, while there might be a case for recessed bolt heads in some instances, there isn't a need in a No4/5.56 conversion. But that's only my opinion and as I say, I'm an Armourer principally and an engineer secondly but not a gun maker or gunsmith (how I hate that cover-everything term.....)