The floorplan is a bit odd. Is the second bedroom actually a converted dinning alcove?

Could be. The apartment was carved out of an original eight-room: http://digitalgallery.nypl.org/nypldigital/id?417246

The old apartment's second bedroom and a piece of hallway became the new C-line's kitchen and the little DR/BR. The old kitchen became a BR, and the huge main bath became new bath, hallway, and closets.