Moria and Erebor weren't taken by massive Dwarf armies but small parties of veterans. I think Tours and Tournaments' travel system would go hand in hand with a Dwarven expedition system. Where you could lead a group of Dwarves to try and establish a new dwarven hold like Thorin and Balin.

Expeditions: Can declare an expedition on any mountain duchy not currently owned by Dwarves. Other Dwarves may decide to start expeditions themselves, which you can fund or even participate in. You, your knights and friends will enter travel mode, now having to make the trek from where you currently are to your destination.

Upon arriving your party will need to fight the local leader and their knights. Should you and your party win, you'll take their duchy as your own but lose your old titles. Should you lose, you'll either die, be captured or be forced to march back home. You'll now have to contend with a very upset local populace... or perhaps worse depending on the locale. Not to mention the nearby neighbors who'll no doubt see this as ample opportunity to take the lands for themselves.

This will allow Dwarves to try and retake their ancestral homelands and perhaps even more... should the Dwarves of Erebor want to take the fight to Mordor, they could fund expeditions to it's mountains. High certainty of death. Small chance of success. What're they waiting for?