Hello Michael, Persistent key value stores are not really a one size fits all, so in cases like what you mentioned, I really wont see them as the best alternatives. Instead I will use distributed key value stores like like redis, or even more traditional databases like mongo db.
But that being said, a workaround would be to write a microservice layer over the key value store, and have the different server instances connect to that microservice. I would also use a message queue like nats or apache kafka over the store, so writes go through the queue, but reads could happen directly.