When the installation script requested my database credentials, I entered the credentials for Site B.
The restore process seemed to progress as desired until about 80% complete when a server connection issue interrupted the process. Akeeba displayed a popup that sent me back to the beginning of the installation process, but the connection error persisted. With no other way to get out of the installation loop, I was forced to remove the installation script.
Unexpectedly, after that failed restore, Site B ended up being configured with the same database as Site A; both sites are using the same db. Therefore, I don't have an Akeeba log or bug report from that installation attempt to submit.
I'm not sure what went wrong, or if I was using the correct/best method to achieve what I wanted. Please advise.