I know this isn't the most popular thing to say but I would just use the music you want until a cease and decist order comes from the publishing company. They aren't anywhere near as thorough as APIC.
If you wanna go the legal way go to
http://www.ascap.com or
http://www.bmi.com . Almost all of popular music is represented by one of these two companies so you can find what you need and put in a request at these sites.