You should be able to find all of these in the fabric district easy-peasy. Well, at least you could 6 years ago when I lived there. Just take your list in and ask.
Sounds like a fun project!
No one seems to have the tear away, found resources on the horse hair and cotton batting on Gertie's site. Steinlauf and Stoller, 239 West 39th Street. The real challenge is there only open 8-5 M-F and I work a full time job. I may just walk around Saturday and search with list in hand. Thanks for the suggestion.
Non woven, non fusible interfacing usually works just fine for tear-away in my experience.
Horse hair (well, the plastic kind) is pretty standard - even dreadful Spotlight (like Joannes) sells it in NZ, so I'd be really surprised if you can't find someone who does in NYC these days. Same with cotton batting.