I'm pretty sure you could use Cross Cluster Search. See the docs below. You would configure the monitoring cluster to give access to the compute cluster. Then in the Dev Tools Console you would use an index pattern that includes the remote cluster name like compute:my_index
https://www.elastic.co/guide/en/elasticsearch/reference/5.5/modules-cross-cluster-search.html
Let me know if you need help with it.
Regards,
Lee