I really dont think its going to work. 1st you have the hook up problems, 2nd you have the fitment problems. If I remember correctly, the b13 controls are longer in width and smaller in heigth. Unlike the b14 witch is shorter in width, and shorter in heigth. Maybe with some custom fiberglass work you could make it fit, but the lines and mechanics might not work with your heater core.
Why dont you just go out to your local junk yard, or look in our classifides and see if someone is partign out a b13 or is selling what you want. If you find one at a junk yard you can get them pretty cheap.