Replacing sash cords
Have you looked very carefully at the jamb about 6 inches up from the bottom. The cut in the jamb could be obscured by paint or covered with a zinc weatherstripping.
Since you have already removed the casing, assuming a wide molding, removing some plaster should not create a problem. It might be easier to install replacement aluminum jamb liners, depending if you like the look of them or if you want to keep it original.