Why would a weaker AMOC lead to more transport up Norway instead of Labrador?
My understanding of that:
1) Overturning happens when the surface water becomes (slightly) denser than the intermediate water beneath it
2) Weaker OC implies a water column that is less dense (particularly in the surface layer)
3) This further implies a higher sea surface height (more like a less pronounced depression in SSH)
4) Gradients in sea surface height influence ocean currents, particularly in areas where the sea bed is at ~500m depth - such as the ridges from Iceland towards the SW (along the Mid Atlantic Ridge), and to the Faroe Islands, and also the entrance to the Barents Sea and the ridge NW of Svaalbard
So all else equal a stronger OC in the Sub-Polar Gyre (S tip of Greenland) pulls more of the ex-gulf stream water in the Iceland/Faroe Islands region towards Iceland and spiraling into the SPG, instead of towards the Faroe Islands and up the Norwegian coast. Stronger OC in the area around Jan Mayen pulls more warm(ish) water into that gyre instead of into the West Spitzbergen Current and the Barents Sea.
Conversely, a weaker AMOC in both gyres allows more ex-gulf stream water into the Arctic and Barents.
Basically that ~500m deep ridge from Scotland to Iceland, and SW along the MAR, is a perfect switch that responds to small changes in water density in the deep water regions surrounding it. In deeper water, currents are perpendicular to SSH gradients like wind following isobars, but in shallow water currents can just go from high SSH to low SSH.