You both are correct about the signs on the Patrick's Street entrances to Princes Street, Marlboro Street, and Cook Street. That was my mistake as I walked the Oliver Plunkett Street side only. I apologise for getting that wrong. 
There is no signage on the Oliver Plunkett Street side, or a lowered curb, which would imply there is no through traffic allowed at any time however

Mutton Lane, Winthrop Street, and Rochford's Lane, however, should still be highway=footway in their entirety as they do not have any of the signage, especially Mutton Lane, which can barely fit 2 people, not to mind motor traffic. 

Additionally, Market Alley and Market Avenue, which I did not change, do not have signage and cannot fit motor traffic of any kind. In fact, part of Market Alley is tagged as highway=footway, but not all of it, despite not changing in any way until it reaches the English Market entrance. Refer to the matching Market Lane, which was not disputed in being highway-footway