I found a solution in a VMWare document about sharing a single VM across several users on the same computer.
I don't have the URL, but the gist of it was to move the virtual machine bundle from a user folder to the shared folder. There's more to it than that, but it was relatively simple, quite logical, and it worked immediately. If I'd known what to search for in the first place I wouldn't have had to post the question above, but live and learn.