Can I create a domain-wide singleton service in Weblogic?

We currently have a clustered Weblogic setup for several pieces of our application to reach the usual guarantees in load balancing, fail-over, and so on. Recently, we've added a singleton service implementing weblogic.cluster...SingletonService, which does the job it was designed for, but it seems not the job we require of it. In the current setup there are multiple clusters under the same domain that would need to access the singleton service, but it seems that this does not work.

How can we set up a singleton service domain-wide, that is, for multiple clusters concurrently?

Sanity test: is our observation that the Weblogic SingletonService can not be used domain-wide correct?