Try some cycling friendly “filtered permeability” at Ormond Square. It’s easy enough to do as the square is mostly already closed off to through traffic. It should be trailed at least on the west side as well as the south or north sides of the square (or both of them). A trial should at most only require a bit of tarmac and some signs and paint.
This image shows an example of filtered permeability (photo thanks to the Cycling Embassy of Great Britain) :
And here’s the west side of Ormond Square from Street View:
Bonus points for also trying it at Stirrup Lane, although there’s far more limited benefit there. Image also from Street View: