In case the symlink is the source of your problems, I figured out a workaround. You have to put your symlink in Dropbox, rather than the other way around.
But if you do this, it's pretty quirky. You have to:
1) Make your .../Packages/User folder an actual folder, rather than a symlink.
2) Shut down all Dropbox instances. So, if you have two fixed machines in two different locations, you'll have to do this over some span of time.
3) In each instance of Dropbox, create a symlink out to that machine's User folder. Obviously, each symlink should have the same name, but the actual location of the User folder could be different.
4) Start up Dropbox again.
Now, Dropbox will properly sync the files behind the symlinks.
Note that deleting the symlink on one instance may cause Dropbox to wipe out all the files on the other instances. So be careful.
Personally, I'd prefer that Sublime would just follow the symlinks properly so I could do it the other way around.