First - you are correct: canes look like Caithness canes, but also have been used under different names and by other makers.
Caithness: I don't remember to have seen this weight before (and I have seen thousands of Caithness weights, at least images of them). Also the base finish excludes Caithness in my opinion.
Caithness-Whitefriars, i.e. the Caithness weights in their Whitefriars series, after buying the name: should either have the monk cane with year, or just a monk on its own (not always easy to recognise). Same comment about the base finish.
"Original" Whitefriars: as you write yourself - completely different base.
Edinburgh never made millefiory weights themselves - what shows up frequently as Edinburgh are the series made in 1986 by Caithness in commission. Millefiori weights include an "E" cane, base is flat and marked Edinburgh. A small number of designs only - your weight is not amongst them.
Perthshire: earlier standard millefiori weights did not include the "P-cane ... but to my knowledge these earlier weights had a fire polished base, not concave ground. The actual weights often vary considerably from what you see in the "Complete Guide" - but I would still consider Perthshire very unlikely.
This leaves Peter McDougal and John Deacons, both using this type of canes in their millefiori designs. My "favourite" would be John Deacons - used these canes at least in his J-Glass weights. I have never seen the base, however, so my gut feeling might be wrong.