First of all, "every few minutes the background music changes" sounds suspiciously like my N64 copy of Space Invaders. That, too, had good music, with triggered extra beats and such, and no sound effects off or sound test.
Also, I'm not well informed about the PSP, but Sony was going to start selling UMD-ROM drivers and burners. Theoretically, you could do a direct extraction, but do you know about all my troubles with PS2 direct extractions? Not worth your time AT ALL.
Line-in recording is the way to go.