Sometimes a dealer (or even an independent mechanic) will give you a quote that's ridiculously high, because they've never actually done the work. Maybe they're anticipating problems, maybe they just don't know how long it will actually take. Either way, that's not a good place to take your car.
I'm not an expert on how long this takes, but I've heard people say four hours for springs and/or shocks, and 1-2 hours for the alignment. Dealer rates these days are typically $100-120 per hour, so you can see that the quote you have is much higher than what it ought to be, based on that.
Where (what city or metropolitan area) are you located? You don't show your location in your profile, so there's no way to tell. If we knew, we could probably recommend a place in your area with NSX experience.
I also agree, somewhat, with Koolaid's point. I don't agree that your stock shocks with "turn to mush", but I think you're better off replacing the shocks rather than the springs. Especially if they've been on your car for a while. The Bilstein shocks are a nice way to go, and if you're thinking of springs because you want to lower your car, the Bilsteins have a lowering perch you can use for that purpose, lowering by 7/8". (You can also use them at the stock ride height.)