I ended up using winLAME; I don't really know anything about using source code
Anyways, it worked great! The sound quality's better then the built-in encoder, it's 192 kbs and clocked in at ~4mb! Yay for variable encoding!
I'm also having this problem. I have a song that I think may be ready to submit, but the lowest I can get it to is 6.5 mb before I go under the required bitrate.