Sounds fun for a work day. I occasionally have to do a little work while at Disney, but I definitely prefer to do the work at resorts vs parks. Even 'quiet' spots at parks get a little too busy/noisy for my concentration, and if I need to get on the phone and not just the computer, I feel too inconsiderate for those around me listening to my business call. If I don't want to work from my room, I'll usually find one of the quiet lounge/bar/seating areas and work there. Boardwalk's Bellevue lounge is great, Riviera has tons of excellent spots, Wilderness Lodge has little 'rooms' on the 4th floor overlooking the lobby with comfy seats and fireplaces, so if no one is there, I'll grab those. Boulder Ridge's railway room is also excellent, and if the weather's good, the outdoor seating behind Geyser Point is lovely. Another really peaceful option is Fort Wilderness - I love sitting on the deck at Crockett's Tavern and working there.
When reading, I can tolerate general noise but prefer no TVs near me or sitting at a bar or restaurant where people right next to me are talking loudly - so again I tend to look for slightly more quiet or out of the way spots.
In the parks...at AK, I like the outdoor seating at Nomad Lounge. There's a great little covered hut between Africa and Asia up a trail from the main path with tables and chairs and fans which is a fantastic spot to relax and read. During non-lunch hours, any of the tables in Flame Tree, especially out by the lake, are wonderful spots to read and grab a drink.
In MK, I find the area behind Liberty Tree Tavern with shade and picnic tables/seating to be a peaceful spot to read and relax. If I can score a rocking chair in Frontierland between Country Bears and the
DVC lounge, those are great too. Upper floor at Columbia Harbour House is cool and relaxing, and the 2nd floor balcony at Pinocchio's is a good secret quiet spot. And the tables scattered through the Tortuga Tavern area which is pretty much permanently closed now are a good shady spot as well.
At DHS, the seating area around the closed 'Starring Rolls' is often quiet and not very busy, the covered outdoor tables by ABC Commissary are great too. The garden area across from the exit of Tower of Terror has some nice benches and seating tucked away with a pergola roof and few people wander back there. And benches or even the walls around Echo Lake can be a good spot for reading and people watching too.
At Epcot, I love all the new seating areas around the central hub which add a ton of relaxing spots to work, read, etc. The tables outside Tangierine Cafe are a good spot, you already mentioned Japan's terrace area, the covered concrete benches around the Temple in China are another quiet spot. I'll throw in another great place IF you're a DVC member - any of the DVC lounges at Epcot, MK, and Disney Springs are great - cool, quiet, free drinks and snacks, lots of charging plugins for working too.
