Sounds like a great acquisition alright, cant wait for the pictures ::)....
Regarding "grind on demand". I do it every day with our LSM and from the dimensions you have given for the Cunhill, they would be a very close match I would think. Because of the length of the discharge chute into the doser it is inevitable that several grams of grounds are going to be trapped in there at the end of every session.
All I do is add the quantity of beans required for a session and then add an additional 4-5g. I do a short grind and discard the first 4-5g of grounds from the doser and then let her rip with the remainder of the beans loaded into my Lizzi styled hopper (made from an insulated cup). Not a single grain of stale coffee gets near the FP this way and the loss of 4-5g of beans per session is a small price to pay for perfectly ground coffee.... Bewdyfull ;) ;D