For a 14:55 departure, if I am in biz class or have status on the airline, I would leave Tokyo at 12:40 myself and still have time for the airport lounge. Except at the start of Golden Week or something like that, I have never needed to be at the airport 2 hours in advance.

They recently improved the JR office traffic flow in terminal 1. There are two positions for tickets and pass exchange orders and a separate person just for the N'Ex/Suica deal.

I find the Hakone area rather touristy, but it's Japanese-tourist oriented, so you may find that interesting. You certainly can activate your pass and go to Kyoto on arrival. Since you are flying DL, you won't have cheap choices to fly domestically, train would be next best. I might be inclined to do Hiroshima/Miyajima a bit later in the trip, a day or two without long train travel might be nice on arrival.