Can I still get the path rewards if I own physical copies of both games?

At the crystal ball in my castle there is an option to receive some bonus rewards. These include "path" rewards, which I have read are bonus for having different versions of the game (Birthright/Conquest/Revelation). I have physical copies of both Birthright and Conquest and have played a save file through to chapter 6 in both to gain access to my castle. However I do not seem to be able to claim the path rewards.

Is there a way to get the path rewards without buying a digital copy of one of the games?

Unfortunately, I do not believe there will be a way to redeem path rewards with two separate physical copies of the game. I believe the same is true if you purchase a digital of each game, as well.

On the Start Menu, there is an option Explore Fate where you can purchase the opposite path of the game you own. If you purchase the other route this way, the second path becomes available through the same application, essentially making both paths parts of one game. Because there is no way to do this with the physical copies, you may be out of luck.

It would seem the only way to recover from this is return one game and purchase the other digitally (at reduced price, too). If that isn't an option, you could try and track down one of the collector's editions which contain all three paths (Birthright, Conquest, and Revelations) on one physical cartridge.