The conversion flow should be supported for organization owners, but it can be blocked by organization or enterprise policy.

GitHub's docs call out two details that fit this kind of failure:

• an organization/enterprise can restrict adding outside collaborators
• after conversion, the user is removed from organization/team membership but keeps repository access that was direct or came from former team memberships

For the members where the UI shows the "few minutes" banner and then does nothing, I would check whether outside collaborators are restricted by enterprise policy and whether those users are managed through SCIM or Enterprise Managed Users. If those settings look correct, try the REST API conversion once so you get a concrete error instead of a silent UI failure, then send that error plus the affected usernames and timestamp to GitHub Support.