> - You can only encode to FLAC. Because of the lossy psycho-acoustic nature of Mp3 encoding, it strips out the inaudible part of waves that you apparently need

This is not correct. You can lossily compress the audio that produces binarual beats and it's just fine. All it really is is two pitches being played, one of the left channel and one on the right. The two channels play tones that are almost the same pitch (but not quite, usually separated by 4-20 Hz). There's no inaudible part of the waves. Two sine waves work great, with no harmonics, and nothing inaudible about them. Unless your mp3 encoder is changing the pitch of the sine waves (which it isn't), it will work perfectly.

You can find all sorts of (compressed) Youtube videos with binaural beats that are reproduced correctly.