All of which would be easily worked around if I could ssh into the VM from the Mac. Talking to one of the class TAs (confirmed by a little Googling) tells me that adding a "Host Only" network interface (or changing the existing one to that type) should make that possible. But when I try, Virtualbox's GUI gives me a not-useful error message and leaves the "OK" button greyed out.
So I got out my Yak razor and created a fresh VM. And got the same behaviour when I it up with a host-only interface. At which point I considered looking for the I'm-sure-it's-here-somewhere command-line interface, which would presumably give me a better error message.
And then I dropped my razor and backed away from the Yak, leaving behind the tiniest of bald patches.