I might be misunderstanding you, but this is what I advise for VBR MP3 creation (discard the Audition MP3 encoder entirely and just export to WAV):
1. Download LAME 3.96.1 from here:
http://www.rarewares.org/mp3.html (go to "Encoders/decoders built using LAME 3.96.1," then download the bundle)
2. Unzip that into a directory (say, C:\Program Files\LAME)
3. Download RazorLame at
http://www.dors.de/razorlame/download.php
4. Unzip RazorLame into a directory (\LAME should be fine)
5. Open RazorLame. Go to Edit -> Options, and find lame.exe from step 2
6. Go to Edit -> LAME Options, then the Expert tab, then under "Custom options" enter the text "--alt-preset standard" verbatim as in the quotes. Check the box "Only use custom options." Hit OK.
7. To use RazorLame drag and drop, or use the Add button, to find .wavs (that is, export wavs from Audition and then drag them to here). Hit Encode and then it'll encode an mp3 to the same directory as the wav is from (though that's a configurable option, and you can also elect to have it delete the wav after processing the mp3).
the "--alt-preset standard" option tells LAME to encode with VBR. Most songs will fall in the 128-212kbps range, but in my experience it's usually 128-170kbps. Will sound fine. If you don't think it sounds fine, you can use "--alt-preset extreme" in step 6 instead, which will discard less audio information for the mp3 compression. APS (as it's called) is a good compromise, however, suitable, certainly, for SongFight. You'll have to edit the ID3 tags manually, but this will do the MP3 compression right.
HOWEVER, and this is more what you're asking... if you don't want to do that, you can forget the --alt-preset and "only use custom options" shit. Instead just navigate about the tabs: under General, hit up 128 kbps, mode Joint Stereo. Under Advanced hit up optimization: quality. Under VBR, it's probably wisest to enable it, and then you can make the maximum bitrate 128 (if you want to use smaller block sizes only for stuff like silence) or 160, or 192, or any other value (and then it'll behave more or less like APS). Under "Quality" there's numbers from 0-9: 0 is the most kbps and 9 is the least. Default is 4 and that should be fine. You can use ABR instead of VBR and go for 128 kbps, and that might be better for what you're after. But definitely use ABR over CBR if you aren't going to use VBR. It'll be a negligible difference in file size, but the quality should only be superior.