If you put the LAME binary files into VUPlayers directories you will have the cleanest and easiest front end to managing audio compressions available to PC users. (It isn't available for Apple) http://www.vuplayer.com/ 1) Export a WAV file from HA/MA 2) Add the exported file to the VUPlayer. 3) Right click on the file title and convert from any format into any other and back again. 4) Tag the mp3 file with a right click / file information.
To be fair to the HA/MA mp3 constant bit export, you can certainly create an audio file transparent to the wave output if you make a large enough file with a sufficiently large sample rate. I do use LAME and VUPlayer however