Sounds like you have been shifted!
If they have been replacing parts from trial/error then realised it was a different component causing the issue then only pay for replacement parts that are worn. I would have a chat with the main dude and get him to break it down.
As above poster said, don't pay till your happy, give it a couple of rides first - You say you have spent loads there it's the least they could do!
It does include the shifter , the only thing that they may of replaced which maybe didn't need replacing was the rear mech as the chain, cassette and front ring needed it. Brake pads needed and I asked for the pedals to be swapped as well.
Although I will check they haven't kept the charge on for the jockey wheels they replaced as they have chucked a new mech on. If anyone is interested I'll post back after I've picked it up.