Its the mp3 formatting that is giving you grief. It's known that different mp3 engines generate differing amounts of silence at the beginning, and to make it worse some remove a bit during decompression to compensate, so it can get messy. If you both use the same codec it shouldn't be an issue, but there are a bunch of codecs out there. Having the click, even for just the first bar *should* make it easier to realign.

Safest way is to work with waves, or ape files that decompress to exact copies. Or Flac.

Using Track - export track to file should work as long as you answer yes when it asks to include silence at beginning.

I do not work here, but the benefits are still awesome
Make your sound your own!