Two-way copies using the Synchronize panel will always use the file dates to decide which files to keep/copy when files exist in both sides.
Instead, I think you'll need to use two normal file copies, one in each direction.
You can create a button which automatically skips existing files without prompting you to make this more convenient:
Copy WHENEXISTS=skipYou could probably also hardcode the source and destination paths into the command, or even put two copy commands (one going each way) into a single button to do the sync in one click... before we go there, though, give the simple button above a try and see if it does what you need.
PS: See the Toolbars 1 video tutorial if you want to learn how to create your own buttons.