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You've eliminated all your options for fastening the quarter round. I would glue the side of the quarter round to the wall, then just run a bead of silicon caulk along the edge on the counter since I gather you're afraid of damaging the counter not the wall.
Maybe double-sided tape on the counter top would work. It would not damage the formica when removed. Just about anything you used, including double-sided tape, would not be good on plaster walls. Hope this helps!
I agree with Sharon. You can even use the 100% silicone instead of adhesive. It has excellent adhesion and can be removed with a razor blade