Hi nick, welcome.
I think that in some ways you've already answered the question; that the issue of rights and performance fees is likely to be a stumbling block for the time being, certainly with EMS, which uses commercial CDs as part of its material, and wasn't there an archive CE fairly recently which was taken from CD, too? Bearing in mind that R3's archives in general have created something of an issue regarding the plans for programme on demand, I'd guess it's likely that until that whole question is sorted out, podcasts of the majority of R3's music-based broadcasts will remain a dream.
Just in passing, I wonder if you've reached this board believing it to be the official BBC R3 board? The reason why it has r3 in the title is a tad long-winded, but just in case that was what you wanted, you'll need to visit this:
http://www.bbc.co.uk/radio3/(though we very much hope that you'll become dual-domiciled, as are many of us here....)
Ron