Restrict access to my Azure blob container from Elastic Cloud static IPs

I have a working Elastic Cloud deployment (as an ISV) on my Azure subscription. I am using the platforms' Azure blob connector to sync documents from a Blob container to Elasticsearch.

Since the ES deployment is not on my Azure subscription- I want to secure and restrict access to my Blob storage.

On the face of things I have two options: either use a PrivateLink or specify IP filtering on my blob storage based on the Elastic Cloud static IP list provided here.

When I configured the static IPs in the Blob storage networking pane and tried running the Blob storage sync, I got an AuthorizationFailure; Unfortunately without specific details.

Is what I am trying to do even possible or is PrivateLink my only option? Perhaps there is some other IP range I am missing.