What's the least expensive way to get written permission from
copyright holders to use excerpts of copyrighted audio?

To some extent, it depends on the type of audio. You'll likely be able
to obtain rights to spoken word at less cost, and often with greater
ease than to obtair permission from music. But the sad fact is that
there really is no clearinghouse for audio excerpts whether music or
spoken word. I've written an article for Nolo.com that describes the
difficulties in obtaining permission for audio samples and you may
want to check it out at
http://www.nolo.com/lawcenter/ency/article.cfm/ObjectID/D788BAEE-8E99-4825-B0B97B2D132AF98F/catID/E99ADB31-C4B6-4645-87DEC821D1D5548C
rich