Troubleshooting replication issues is best left to the experts; and since you have already opened a case with Microsoft; that is who you should stick with for replication issues. Provide any logs they require; and continue to work with them to address the replication issue.
That said, you indicated "the customer wanted" to expand the primary with a CAS. What were the technical reasons for doing so? There are very few technical reasons for having a CAS. The only technical reason I'm aware of is total client count. Are they nearing or past 150,000 clients?
If not; perhaps the design may need to be re-evaluated. You don't need another primary + a CAS just because you have multiple domains.