You reminded me of the situation, when I took my car and asked how much would they charge to drain and refill coolant.
First question was, 'is there any problem' and I said 'No, I am getting it done for my satisfaction'.
Now he started thinking of hours and coolant price and I was told, it would cost about £400-450.
I asked him, why is that. The response was, they would have to let the car cool down, drain it, refil it, bleed it and return it and hence £400-450.
I ended up buying coolant only and got it done at my local indy.
I am sure you will get it done by them as it is very fair price (NOT).