I followed Brian Lane's suggestion about issuing a Load Config command
and then sending bogus data, followed by normal Read Program Memory
commands to get the ID and config data, and it worked!  Thanks, Brian.

In response to Derrick Early's message, I'm not particularly worried
about overwriting the ID info, but I'm terrified of accidentally
setting the Code Protection bit.  I don't have a parallel programmer,
so once CP is set, the part is no longer programmable.  (If you're
listening, Microchip, you should add a serial-mode command to do a
bulk erase.)

d.