I've recently started to shoot weddings, only a couple under my belt so far, but my gear is somewhat similar to yours. D700, ai 20/4, 35/1.4G, 85/1.4G and the 70-200. Always a rented second body.
I bought the 70-200 to use at weddings. It's huge (which is okay). It's heavy (also okay). It's versatile, yes, BUT, I'm slightly struggling with it. Mainly because of me being accustomed to primes, handling and seeing that one perspective, always knowing the frame before I glance through the viewfinder, using my feet and moving to get the image right. I find it hard to get used to zooming and have been thinking about ditching the 70-200 in favour of the 135/2. Yes, the 70-200 gets the job done, but I'm much more relaxed and take shots that are much more "me", and thus better, when I throw the 70-200 aside and continue with the 85/1.4. Weddings are of course fastpaced events where you can't miss a shot, but I have not felt at all hindered when the 70-200 has been in the bag and the 35 and the 85 on the cameras. Mostly the opposite actually.
Of course, you might not feel any different strapping on a 70-200 instead of a prime, but just as a heads up, something to take into account as you seem to be in primeland too.