I had a similar issue few months ago and updated the Brightcove dialog to resolve the issue. I don't believe there is anything that can be changed from AEM side to fix the issue.

Can you check if the dispatcher is blocking this URL on the publish tier? If that's, not the case, try rebuilding clientlibs to clear the cache.  [1] https://helpx.adobe.com/experience-manager/kb/How-to-force-a-recompilation-of-all-Sling-scripts-jsps-java-sightly-on-AEM-6-4.html

If you want to use third-party monitoring apps, I would recommend either using New Relic Or App Dynamics. I have worked with both and very easy to install.  [1] https://docs.newrelic.com/docs/agents/java-agent/additional-installation/install-new-relic-java-agent-gae-flexible-environment#tomcat-examp...

If you have a valid AEM license, you can download the jar file from "https://downloads.experiencecloud.adobe.com/" For users, you could set a boolean property named "external" under the user's profile node(/home/users/****/profile)and map it to SAML property or set is using custom code.

If you are trying to automate it, you can simply use the lock/unlock processes as part of a workflow. That way the same system user will lock and unlock the node. 

If you are looking for specific permissions, its "jcr:lockManagement" and you can add it from crxde "Access Control" tab Or from the new user management console if using 6.5. See below for more details: 

Go under crx-quickstart/install directory and you should see "org.apache.jackrabbit.oak.plugins.blob.datastore.FileDataStore.config". That config file should have the path to datastore. By default, datastore is under crx-quickstart/repository but thats not the case here and it seems to be somewhere ...

Can you check I datastore directory is outside of the default AEM folder? Also, check the JVM tmp directory

I had a similar requirement(search with jcr:uuid)and just adding the jcr:uuid to the index worked. 

We have Query Manager tool that can be accessed from [1]. It will show the slow/popular queries and how many rows each query traversed. [1] http://<host>:<port>/libs/granite/operations/content/diagnosistools/queryPerformance.html