Unfortunately, so am I! Have you had any luck at all since you posted this?
One of my Great-Great-Great-Grandmothers was (I hope I counted that right) Catherine Maria/Mariah Groesbeck Burns. I think I've looked at the same census records you have, trying to figure out who Rebecca's parents might have been in the Stillwater, Saratoga Co., NY area in 1820/1830 (based on the statement in the Isabella Co Inquirer obit for Henry Groesbeck about their origins). I'm a stitcher, in addition to being far too buried in genealogy, and am trying to do something called a 'Mother Tree' - which is direct female line only. I'm wistfully hoping someone knows Rebecca's father's name, so I have at least a CHANCE of finding her mother's name.