Please support replication between sharded clusters. This would effectively first require multi-master replication behavior and support to exist.

One Idea:
Good idea to use an existing op-log for cross-cluster replication. Read from op-log from each shard and apply the operation on destination mongos (another datacenter).

The problem is in the same operation will appear in destination cluster op-log and infinite loop will start as a result.

The solution is to append to document a special marker to specify the appurtenance to the particular cluster.