The I A C is the Institute of Amateur Cinematographers, their website is
www.theiac.org.uk
They have negotiated with the British Phonographic Industry (BPI), The Mechanical Copyright Protection Society (MCPS) and Phonographic Permormance Ltd (PPL) for IAC members to buy from the IAC licences to enable them to use commercially produced music in the circumstances outlined above. As one of the agreements is with the British Phonographic Industry, I imagine this only applies to UK produced music. Whether residents outside the UK can join the IAC, I also don't know.
Here's the specific page of the IAC website
http://www.theiac.org.uk/central/copyright.htm
Other countries may have a local equivalent of the IAC - I did a quick websearch but of the two USA sites I found
http://www.ampsvideo.com/ and
http://www.ammaweb.org/
neither mentioned a similar scheme, even though they have web links to the IAC site (and in the case of the latter, my own local video club, Surrey Border!!) Join and start lobbying perhaps - or at least email them and find out whether it's been tried.