Sharing your Beersmith folder between PC's using a file syncing service actually works quite well as long as you take care not to run the program on both PC's simultaneously.
Keep in mind this is completely unsupported, you may lose all your data (although it never happened to me in the 3-4 years that I've been using this method) and you may have to manually sort out conflicts in case you accidentally do run them at the same time.
I sync my entire .beersmith3 folder with the exception of BeerSmith3.txt between 3 PC's using a tool called Seafile, but it should work with Dropbox or Syncthing as well. I don't remember why I put BeerSmith3.txt on the ignore-list, but I guess there was a reason.
Again, I wouldn't recommend this unless you have good backups and confidence in your ability to sort out problems, but if you like to live on the edge...
