I'm doing exactly the same (just for the experience; no, I don't want to
buy a commercial programmer) and ran into the same problem.

As far as I can find out from the microchip documentation and some software
from the web the correct command sequence for reading the configuration is
- issue a 'load configuration' (with dummy data), now the PC points to (the
first entry) of the configuration memory
- now DO NOT issue 'begin programming'
- issue a 'read data from program memory' which will now read from the
configuration memory

You could read this from p4 of the 16c84's 'EEPROM memory programming
specification', but I understood that section only when I saw how someone
else did it.

Success,
Wouter.