I cleaned up 2 other kahane audios (one was the shiur at YU and at the national press club) a month ago using audacity. I'm the one who used a high pass and low pass filter at 300-3500 hz and then put them through sound filtering. I gave them to yukutiel but he didn't post them yet. They sound really good. Hopefully he'll post them soon or I'll be forced to post them myself.
So use the high and low pass fliter then eliminate the background noise (be careful here and go mild since if you do it too much part of the audio will be eliminated and it will sound like a telephone call) . It helps to also amplify the sound when you are done and possibly use a plug in called "leveler" (for audacity) at the low setting to even out the audio if it is too dynamic.
Audacity is a great program. I'm working on a Kahane song with it.