Hey Chief... great post... and you probably aware that the engineer/baggage dude can only shut down the APU from the wheel well... of course you did..
As to Areas of Responsibility.. Vol 1 NP11.6 - 11.7 clearly show the Engine Start Levers and Fire Warning Switches being a 'Joint Responsibility Item".
In our company though, we run the appropriate checklist with same responsibilities on the ground as if still in the air.. ie.. Fire Warning on the ground is treated the same way as Engine Fire Severe Damage etc etc as in the air.. thus Capt performs A/T disengage, thrust lever closed, then FO follows with the rest.....