I had the 16 AT flash. It was the Duty C Solenoid alright. The actual solenoid costs around $100 and comes with a small gasket for it and a large gasket for the trans extension housing. Also get some Red Permatex.
It takes a while to get into the extension housing. You have to remove the exhaust pipe, the central drive shaft and them the many bolts for the trans extension housing. Once you pry open the housing you'll see the solenoid. Remove the old, put in the new with the gasket and permatex, put on the new large gasket and permatex and them put everything back together.
I started one night around 11pm and finished around 6pm. I worked pretty much straight and one of the senior mechanics helped me put it all back together. We stopped for coffee a few times.