Also (unrelated to this), the reason the children's tickets are and always have been age 6-12 is because that's the age cutoff for normal train tickets for almost all companies all over Japan. (Older students get discounted commuter passes but that's not directly linked to age). Easier to keep things consistent I guess.
Children’s tickets are 6-11 by the way. At 12 they’re adults.
Our next trip is for a month and I had already looked into commuter passes to lower day to day travel costs. As you say, the “young adult” discount is related to there being a certifiable school address involved. Cheapest option (which myself and the kid are elegible for albeit not dad or granddad) looks to be the combined Tokyo Metro/Toei Subway ticket -
https://www.tokyometro.jp/lang_en/ticket/value/travel/
If used over a three day period it’s 500jpy a day, same price as an all day Toei Bus pass.