hmmm. I probably qualify more of a Japanese train geek than an AV geek. A few of my takes
1) 24 hrs is not enough
2) Being in Maihama, you might try the Subway museum which is closer than Saitama. Maihama is tough.
3) You can probably catch the NEX with 40 minutes in Narita. But transferring to Keiyo is a TREK. It is like going from one end of a big airport to the other end. Its really far. If you were not hell bent on the NEX, I would take some combination of local trains to Maihama.
4) Train swaps in Shinkansen are not common. You can probably catch any hokuriku shinkansen for W/E 7s. Anything that goes to Hakodate will be H/E 6s.
5) Worth it for green car? In your case, I would probably say yes, only for the kid. For the W/E 7, there is also a Grand Class. The regular train green cars may be more fun, as they're double deckers. From Maihama, if you're not dead set on Shinkansen, taking some combination of musashino line/tobu/keihin tohoku might be faster/more interesting. Omiya to Ueno local trains have double deckers for Green Cars. Go for it. $7 USD equivalent. Only E4s are double deckers on Shinkansen, and I believe they're all going to Niigata and back. If you go to Saitama train museum, they show exactly which trains are which types and they have a timetable for when they pass Omiya.
6) As close as you are to Disney, its going to be hard to pass that up
7) The Hatchobori I think is doable. I wouldn't sweat the details on that as 4:15 to Hatchobori to 5 PM ueno should be easy. May be easier if you go to Tokyo and take Yamanote or any other option.
8) Probably not for this trip, but the Tobu train museum can be fun too.
9) This youtube channel might be interesting for your child
https://www.youtube.com/user/suzukawaayako