I wrote earlier that I recall hearing that records made in the U.S. before 1972 were not protected by federal copyright. But I also pointed out that (assuming that what I heard was correct) for records made prior to 1972, state anti-copying laws might apply. Also, even if the record isn't itself protected by copyright, the music on the record might still be.
What the law should be, in my opinion, is that what annap proposes would come under the heading of "fair use." But I fear that that is NOT what the law will become if the question ever comes to court. The copyright interests have been fairly successful in using the courts to narrow the definition of fair use. The law states that "multiple copies for classroom use" is a fair use. But the publishers have gotten the courts to rule that it is NOT a fair use for a copy shop to make the "multiple copies" in exchange for money at a teacher's request.
Similarly, for scientists to copy journal articles from library copies of scientific journals for their private use has always been considered a fair use. But the copyright barons have gotten the courts to rule that, if those scientists work for Texaco, a profit-making corporation, this use is NOT fair--or at least, less likely to be fair than otherwise.
Again, the law creates a "homestyle exemption" from music licensing for business owners who want to bring home-style audio equipment into their shops. The barons have gotten some courts to interpret this exemption fairly narrowly, and I have a hunch they may also be preparing to attempt to destroy the homestyle exemption altogether through the back-door of the WTO.
Because of these complications, if I were in annap's place I would consult a lawyer before going ahead with the project.