Snow Leopard Server in Fusion VM: installation keeps failing

I’m trying to install Snow Leopard Server 10.6.3, which I just purchased from Apple (so it’s not tied to any hardware), into a VMWare Fusion 5.x VM, and the install keeps failing.

At first I was getting “ERROR_DOWNLOAD_FAILED” as the reason, so I disabled the network adapter for the VM to see what happened. At that point, it failed with the even more helpful “support files could not be installed”. That’s it; it didn’t bother to tell me which support files, just that they couldn’t be installed. When I tried again, it went back to “ERROR_DOWNLOAD_FAILED”. I turned the network adapter back on, and failed the same way.

I’m using the default install options, which should require a little under 12GB, and the VM’s HD has 43GB available. The machine I’m running the VM on is a MacBook Pro (i7) running OS X 10.8.

Any insights are appreciated!

EDIT: see my answer below for the resolution, which required two steps.

I found a link that might help: https://communities.vmware.com/thread/457351

You have Server, so that should be OK, try ripping it into a disk image (if you haven't already done so) and see if it will work with that instead.

I only have personal experience with Parallels, so I can't try it myself.