AWS Lambda & API Gateway: Custom domain names, Route53 and different roles


I’m looking for advice on how-to solve following problem:
I’m building multiple APIs on AWS using AWS Lambda and API Gateway. Client wants a custom domain under which all of these standalone APIs are to be mapped. There is a guide to this here:

But my case differs here. My APIs and Lambdas are deployed under different account than the Route53 resources are. Client can provide me with IAM role with which I could do the actions needed to be done in/on Route53 with serverless-domain-manager but I have no idea how to do this with serverless and/or serverless-domain-manger. How to set this up? I could use some tips on what I should do if serverless is not up to the task and need to set this up manually.

Thank you for your help in advance.