Welcome back to the QuickBooks Community, TL1960.

I'll provide details on how user access works in QuickBooks. I'll also ensure that your organization's data permissions are properly managed.

As mentioned by 4Gal, you need to request to transfer the role of the Intuit Account's primary admin from another organization to yours. To do this, you have to coordinate with the person and this admin will request to us to move the role to your team to help maintain the security of their financial data.

On the other hand, you're now on the right track in assigning the roles. The Bookkeeper might added as a Full access user since this person needs unlimited access but no administrator privileges. Then, you're right about assigning the Company admin role to the board chair as she won't likely go into QuickBooks but will always be able to if necessary. Then, transfer the Company admin role to that executive director once hired.

Lastly, the admin can add you as the report-only user since you're only a signator on checks on the program and handling reports to keep an eye on things. To see further guidelines on how a specific role and access are organized in the program, you can read this article and share it with your organization: Create and manage users and roles in QuickBooks Desktop Enterprise. This also provides steps on how to customize each role and give individual permissions for specific tasks. 

In case your organization needs further procedures for effectively managing your business using QBDT, you can read this article: Help guide for QuickBooks Desktop.

If you have any additional questions on managing users in QBDT or other related concerns, you can add them below. I'm always here to help, 

TL1960. Have a great day!