will Shimano Shimano Dura Ace 7700 STI Flight Deck work with Rear Derailleur Shimano XT RD-M771 I thinking to change my Long Haul Trucker set up. Have both Dura Ace 7700 / 7703 STI Flight Deck 3x9. Will it be compatible with the LHT stock Front Derailleur Shimano Sora FD-3403 n Rear Derailleur Shimano XT RD-M771.

I'm changing over to Paul Touring Canti's brakes too. Just wondering what other issues might come up

Sorry if these questions are redundant. 
Thanks for your time and consideration.
Yes, all nominally 9-speed Shimano mountain RDs will work with ST-7700, and all pre-11-speed road FDs will work with ST-7703, except for FD-4700 at present and any future 10-or-fewer groups that use the 11-speed actuation ratio.