Making an ID of a board type
You say a micro in the base unit needs to identify the board type, and that these plugin boards already have a IIC bus going to them.

This is a no-brainer.  Put some device the micro can detect on the IIC bus at a unused address.  The easiest would probably be the cheapest and smallest IIC EEPROM you can find.  In manufacturing you can write whatever information you want into the first few bytes of the EEPROM.

You say you don't want to use a EEPROM or a micro, but give no justification for such arbitrary and seemingly silly restrictions.  We can only assume this is then for religious reasons, which have no place in engineering.  Do your job right and use the best-fitting solution.

I just checked, and the Microchip 24AA00 16-byte IIC EEPROM is available in a SOT-23 package and costs 18 cents in singles, 14 cents in volume.  All you would need is this chip and a bypass cap.  You'd have to come up with a really good reason this isn't a good solution.