The collection at Lincoln Center Library is quite extensive (and apparently there is a smilar collection in Washington - I remember hearing they taped all 6 of the Sondheim Celebration shows 3 years ago.)
To view a show you have to present a good reason for seeing the tape: a teascher, community theatre producer, student doing research etc. (In other words just showing up with nothing to do is NOT a reason.) I believe you also have to make advance reservations. Some shows are restricted and you need specal clearances from teh authors to view.
The collection began back around 1970. Not every show has been preserved but a good number have. Be aware that these are "archival" tapes, so not having the advanced video techniques used in commercial releases. It is mostly a 2-cam set up. And none have been cleared for commercial release.
Here's a secret not many know: In the Rodgers and Hammerstein archives are 16 mm films of the original productions of ANNIE GET YOUR GUN and SOUTH PACIFIC. Wouldn't they be wonderful to have a peak at!
Cast albums are NOT "soundtracks."
Live theatre does not use a "soundtrack." If it did, it wouldn't be live theatre!
I host a weekly one-hour radio program featuring cast album selections as well as songs by cabaret, jazz and theatre artists. The program, FRONT ROW CENTRE is heard Sundays 9 to 10 am and also Saturdays from 8 to 9 am (eastern times) on www.proudfm.com