After some conversation with an AVRDUDE developer I submitted bug #26002: HVPP of EEPROM with AVR Dragon and ATmega8 Fails. This problem was mentioned earlier and while I tried to get the app building so that I could attempt to fix it myself I wasn’t getting very far.
Thankfully I’m able to use the AVR Dragon in HVPP mode (which is the configuration shown above with the many, many jumpers) via AVR Studio and accomplish my goal. This means that programming the chips for the SDrive NUXX kits/parts/assembled devices should go quite smoothly.