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My delta pivot mounts are good I think (two have a touch of side to side play, not much) but I can't find a reference as to how the joint between the arm and pivot should feel. Should it spin freely in the arm, like finger flick? Should it be able to hold the arm and not fall?

A finger flick of the aluminum joint should set it to spinning pretty freely - again without side-to-side slop. This interface was the culprit on my machine.