Hrmmm I remember Bobik talking about border battles as well, but I am not sure if these are going to work in practice.
The sizes of
lands Kingdoms may claim seems extremely limited.85 meters (or 85 cells) in any direction is the maximum size of a claim for the largest, most impressive, most developed of all realms.
Amateur golf players can easily drive golf balls outside of the north border of your kingdom, and land their shots outside the south border.
Your conflicts, then, would only be against your neighbors down the street.
I think border conflicts under these constraints will be the exception and not the rule, unless there is some way to expand territory beyond just improving your monument.