Now then, why did I never find this wonderful resource before? The Answer Lady and Jack have a series of youtube videos explaining exactly how to fix problems like the ones I was having with my garter carriages.
In short, my 'thorough' cleaning hadn't gone far enough. The gunge that was used as lubricant when the machines were first made had become thick and was clogging the mechanism and preventing it from operating smoothly. Once this was all cleared out of both machines they were re-lubricated and are both now running like new.
Details are in The Answer Lady and Jack's highly recommended videos.
