We have an external CRM which contains all our customer information. I would like to integrate our CRM with Jira Service Management so that we can assign Jira issues to our existing customers, being able to view a limited amount of customer data from the CRM when viewing a Jira issue.
In Jira Service Management, I'm able to define additional fields on a customer. 
However, my customer list is thousands long and it's not practical to manually enter all this data or to manually maintain synchronization between systems. There is a CSV import option, but this is manual and I'm looking for a fully automated way to keep information up-to-date in Jira from my main CRM.
I have searched and searched for an API that would allow me to update or retrieve these fields and I have not found any. The only customer related API I found was to create a new customer (https://developer.atlassian.com/cloud/jira/service-desk/rest/api-group-customer/#api-rest-servicedeskapi-customer-post) and to list customers that are part of a service desk (https://developer.atlassian.com/cloud/jira/service-desk/rest/api-group-servicedesk/#api-rest-servicedeskapi-servicedesk-servicedeskid-customer-get).
Is there an unpublished API endpoint that will allow me to work with this data? If I can't find one, I'll have to resort to writing my own Jira app for this, which seems pretty extreme. I would store the customer data as a property on the customer entity (which I can work with via the API) and have an app that displays that data as a side panel when viewing an issue. The built-in customer functionality seems quite under-developed, particularly on the API end.
I did search for existing apps and there may be one I could use for my purposes, but it was designed to solve a different issue.
Perhaps this has been solved and I have just been unable to locate the solution. Any suggestions?