Hello @AlexTuskany1 and @James_Peel ,
A project can not be transferred if there is an active Site Plan (which I assume your Client Billing project(s) has) on the project, so the Site Plan subscription would first be needed to be canceled before you can transfer the project.
Or, you can transfer a duplicate of the project to your client’s Webflow account.
So once the project is on the client’s account, they will need to re-setup the custom domain, however, as the site is already connected there is no delay for DNS propagation and the downtime should be less than a few minutes - the time it takes to cancel the Site Plan, transfer the project, re-purchase the Site Plan, type in domains and click publish.
Hope this helps, and if you need further assistance with this when it is time to transfer the project to the client I suggest contacting Webflow Support.