Hi Tonz, sorry for my slower reply – I’m currently in Japan for some meetings.
Tokyo > Nikko = Nazuno Shinkansen has green car, however the normal train from Utsunomiya to Nikko station does not.
I’m not sure where in Gunma you’re heading, but to Jonokogen from Nikko, both Tsubasa and Toki Shinkansen has Green Cars.
Gunma > Chiba = Both Toki to Tokyo and Narita Express to Chiba has Green Cars.
Your entire route is covered by green cars except for 1 or 2 smaller local trains to get from the shinkansen stations to the cities / stations you mentioned.
Hope it was of help and let me know if there’s anything else we can do to help! We wish you a great stay in Japan 🇯🇵
With kind regards, Jonathan H.