Hi, our experience with FP's at the Tokyo Disney Resort was that the first one you have to wait around 1-2 hours to get a new FP but subsequent FPs you can obtain much quicker... I have some notes from our trip in November that say the following: Our next stop was the Tower of Terror to get some FP’s. We had gotten our first FP at 8:10ish and were able to get another at 9:15am. The FP return time at 9:30ish for Tower of Terror was already 11:25 – 12:15 so we grabbed those. So as you can see we only had to wait an hour to grab our second. The notes go on to say we could get our third FP at 10:55am so that was about an hour and 35 minutes after the second FP. Each day was different, but it definitely wasn't a 2 hour wait between each FP and we found ourselves not needing more than 3 (also by the time you go for your 4th most of the FP's were already assigned - they will mostly be assigned by lunchtime anyway because the Japanese really know how to use the system!). We also didn't run in the mornings. Now we stayed on property (Miracosta) so we got into the parks 20 minutes earlier than opening for Tokyo Disney Sea and 15 minutes earlier than opening for Tokyo
Disneyland. This was IMMENSELY helpful as we were ahead of the crowds. We saw the crowds running one morning and it was like a giant sardine can moving forward at record pace so we were glad we didn't have to experience that. If you can stay on property i'd highly recommend it for that reason alone, otherwise, get there an hour before opening (at least) to beat the crowds as the Japanese know to get their early and always do! Additionally the Japanese parks do have a 'no running' rule (it's written on the English guide map rules) however it seems that the cast members only half try to enforce it. It's so strange because the rest of Japanese society is so stringent about following rules
If you are interested in reading my full Tokyo Disney trip report the link is
here