FreeCommander will allow you to accomplish your goal.
It doesn’t do it exactly how you want, but it has sufficient functionality to get the job done. It allows synchronized browsing. It also allows opening new locations automatically synchronized to an existing location.
The big downside for you is that it only has 2 panes, not 3. That’s not ideal for you, but clever use of folder tabs makes it almost as good. You can drag and drop directly onto any tab just like it was a separate pane.
It allows declaring a root dir across all the systems, has drag and drop, and even allows you to save profiles. It is very flexible.
It’s not a perfect match for what you need, but it comes close enough that hopefully it will be helpful to you.
UPDATE:
After losing important data due to FreeCommander bugs, I can no longer recommend this application. The developer simply does not perform adequate testing before releases, and does not have any dedicated QA testers. This application has great potential, but overall the project needs a much higher level of QC to recommend it universally.
