Most interesting factor of this claim concept is to me, that there is limited space to build and that one might have to be careful not to waste too much resources to afford the next claim.
The challenge is what makes it interesting!!!
Having to build in a tight place and looking forward for more territory.
Would go for 1 chunk big cells (32x32 tiles).
Would also calculate the price depending on entities within the chunk.
The price might be reduced if there are "bad" things like biters, cliffs or water.
The price might go up if there are resources.
Would count all entities in the chunk and make up prices.
Distance would not even be necessary then since one could just use the resource amount.
Also would make them more expensive the more chunks that you own.
Could be something like a 2% or more increase per chunk owned.
This way the claims could be very cheap in the early game and get infinitely expensive the more are owned.