"I am a little confused about the Tateyama route. The only trails I can find are 2.5km at most, but you mentioned getting away from Murodo and possibly being the only person on the trail for hours. Am I missing something?"
Hi, first, I think what Rick is writing is on the button. I'm not sure exactly which routes you are looking at, but a lot of people when they climb Tateyama, they mean the mountain range Tateyama (which in that sense consists of a couple of different mountains/peaks). So from what I experienced there, people climb from Murodo to a peak called Oyama, which has a toilets, a hut/shop (called Ichinokoshi if I'm not mistaken), and a shrine that you can climb. Then they turn back as this is their day hike. If you continue from there on, you can suddenly be totally alone. From there you can for example climb Ounanjiyama (the highest peak in Tateyama at 3015m) and onwards to Bessan and Tsurugimae, where there will be huts and a camp site. If you want to climb Tsurugi you have to read up a bit on her, and do it in the morning - if you have good weather (lots of rescues from there if I'm not mistaken).
If you can, buy in advance, or once you arrive in Japan, go into a outdoor/climbing shop and get map 36 of the Kita Alps
Hope that helps. Don't underestimate the rainy season, and have fun.