That "stitch, hesitate, stitch" movement you describe is exactly like my 1222 moves...so unfortunately I'll bet good money that your camstack is cracked. To be more precise, the crack probably continues on though the camstack to the plastic gear that drives the camstack, transferring motion from the main shaft. I recommend you take off the top cover, and slowly turn machine through a complete revolution of the LEFT SIDE camstack. I think you will find a crack running from the back side of the camstack to the front.
That's not to say your machine doesn't also need cleaning, but my machine was pretty clean (no excess or old grease in the works), and the hesitation every revolution is caused by the crack through the cams and into the drive gear.
EDIT: I posted this before I saw your update on the apparent cause. Hope I'm wrong, but have you ruled out the camstack as the culprit?
Last edited by Borletti Milano; 02-03-2016 at 10:44 AM.