Don’t know if you’ve already gone on your trip, Â but we got home yesterday from 3+ weeks traveling around Japan mostly via JR.
Our youngest son, who turned 12 (!) during this trip, is multiply, profoundly disabled, medically fragile / complex, severely I/DD. For travel, we have a light (-er) weight red Convaid w/c with sun bonnet which we (parents) push: both for motor planning and cognitive reasons our son is unable to participate in rolling (in any of his ADLs, really).
Okay, I explain my angel so you can picture a human unable to participate in any self-advocacy, and who is a child, an appropriately sized 12 year-old, but not an adult independently manipulating their own chair.
My Japanese is so-so: for a tourist it is excellent, but for a resident of Japan (which I’m not — live in the US Rocky Mountains) it needs work. I had contacted JR over a year before our trip to ensure Accessibility throughout the nation (for example, no elevator at JR Nikko, but they have a special stair machine), and to ascertain that a regular JR Pass would be good for my child. I spoke in both English and Japanese with JR folks about these. I was told that in order to get the kurumaisu seat we would have to get it at the station from which we were departing, and not the day of travel.
At the JR counter in Ueno as I was planning our day trip up to Tochigi I was told my child is not entitled to a kurumaisu seat because he is a child. This makes no sense, of course, as he is not an infant or toddler in a stroller purchased from Babies-R-Us! He is 80lbs and 4’7″ long. But that’s what we were told. So for that trip we just went with non-reserved seats and relied on the kindness of those seated nearby to adjust so my husband and I could sit near our youngest (our eldest is 13, so he was delighted to sit by himself for a bit).
Then at Tokyo eki I was told my son could jot have a kurumaisu seat because they are reserved for shougaisha  (handicapped). Um …. So I explained, in Japanese, my son’s myriad disabilities, and was shut down because my son doess not have a Japanese Disabled certificate. She (JR lady)  then told me the kurumaisu seats are only for nihonjin — Japanese people. I told her that’s not true and asked to speak to the supervisor;  she refused. I asked another JR reservation agent and they would not get involved. We had already been at that counter for an hour, kids were bored, so I gave up for that day. (But in my head I was furiously swearing at those idiots.) They were wrong, but you know what? My children are hapa (half-Japanese) as their father is issei, first-generation Japanese.
In Takayama eki we were told the same thing by a station guide (who held the slope), that kurumaisu seats are only for Japanese. He then tried to wrestle my son’s chair away from my husband to shove it down a too-narrow passage on the train. I yelled, in Japanese, for help, Â and the conductor ran right over and argued with the station guide. He placed my son in the kurumaisu seat with my huband in the seat adjacent, Â and he apologized to my older son and me that he did not have two more seats right there (we sat seven rows back — it was fine, of course).
The BEST JR reservation experience we had was in small Hiroshima eki; five different agents were involved (they were all young, so I think it was novel for them), Â and it not only took more than one hour, they needed the supervisor to okay it (the kurumaisu is seats, Hiroshima-Shin-Osaka, Shin-Osaka-Tokyo, Tokyo-Narita), so asked me to return the following day.
My son and his daddy did have the private room. It worked out well because the (uncomfortable) bench folds into a bed; my son had a GTC (formerly called grand mal seizure) shortly after we got on that train, so we made the bed for him to have a postictal nap. Now, in case you don’t know, the private room is not only very loud (not insulated as well as the passenger saloons), it is very noisy from people talking on their mobile phones, using the restroom, mothers with crying babies, all outside your door. Â I was told JR prefers to keep the private room for nursing mothers. That’s what I was told, but I don’t know.
In Kyoto while getting ice cream I saw a darling young woman, Cuban, in a self-operated motorized w/c. I chatted with her (traveler, like we were), and she said that while it did always take a while to get her reservation, she did always get a kurumaisu seat. Granted, she was not traveling with others (as your and my families are / did), so sitting with someone was not are priority for her.
So, super-long story that our experience was: in person at the station, hopefully with an informed, capable reservation agent, and to have the w/c passenger there so they can see and accommodate.
Good luck!