Hello Mark,
Once you have verified as a domain owner in Web Central, it is possible for you to delegate subdomains to developers within the organization to do their tasks without having to verify domain ownership themselves[1]. For more information on delegating, see Managing users, owners, and permissions.
The domain name verification is automatically re-confirmed about every 30 days. In case the verification string from your DNS settings is removed for some reason, it will restrict your ability to change the configuration within the Google Cloud Platform Console. This restriction does not change the serving setup for the domain and app continues to serve over the domain[2,3]. Verifying your domain primarily just proves to Google that your application is in fact allowed to receive all the traffic for domain because you've shown that you "own" it[4].
[1]https://cloud.google.com/endpoints/docs/openapi/verify-domain-name#delegating_to_developers
[2]https://cloud.google.com/endpoints/docs/openapi/verify-domain-name#verifying_ownership
[4]https://groups.google.com/d/msg/google-appengine/jhJkoUf4p8M/EuMBw_nbDQAJ
Only the user account that has verified ownership of the domain name can deploy the API initially. After that first API deployment, project members with Editor permissions can deploy it.

Hi Mark,
You are right. Since you are the person who validates the domain, the first time you need to deploy the API. And after that the members with ‘Editor’ permission are able to access that API or deploy a new one. And regarding domain validation record add up, I think you are on the right track