Balancing the load in content addressing schemes for route-restricted networks represents a challenge with a wide range of applications. Solutions based on greedy embeddings maintain minimal state information and enable efficient routing, but any such solutions currently result in either imbalanced content addressing, overloading individual nodes, or are unable to efficiently account for network dynamics. In this work, we propose a greedy embedding in combination with a content addressing scheme that provides balanced content addressing while at the same time enabling efficient stabilization in the presence of network dynamics. We point out the tradeoff between stabilization complexity and maximal permitted imbalance when deriving upper bounds on both metrics for two variants of the proposed algorithms. Furthermore, we substantiate these bounds through a simulation study based on both real-world and synthetic data.