I'd definitely get a second opinion on it through a reputable transmission shop on the diagnosis. Dealerships usually have high overhead on fancy buildings, but everyone uses pretty much the same book for billable hours of labor. So you just make a comparison based on parts and labor rates with the local transmission shops.
Last transmission (4L60E) I replaced was over 20 years ago and I got it for $1800 installed through a dealer with a 5 year 50K mile warranty through GM. I had the clutch replaced this year through the local Ford dealer and it was less than $2K on my 99 F250SD 7.3L.
I realize these aren't great comparisons but they are all I have to go by.
