I’m definitely not top tier is the latest Disney dining info, but I’m wondering if these are theoretical max party sizes, as opposed to practical one? Like, you might get them if you call in, but these wouldn’t really be available to book online? And may or may not be available if you call?
Here is some quick-and-dirty online booking research I did last year:
I just didn’t see many of those sorts of large max party sizes at all, but maybe things have changed dramatically since then? 
. Or, maybe they are available by phone?
I think if it were me, I’d try to book online at 60+10, splitting the group if needed so I at least have something booked, then call and see if they can accommodate us better?
FWIW, here’s how I did it:
Our travel party was 7, with extra relatives joining us to make it 10 for a couple of meals.
I made one leading room reservation and included myself, DH, and DM on the leading. (I have login capability for all 3.)
When needed, I would split our reservation into 2 parties booked online under myself and DH. Booking at 60+10, that got me everything I wanted.
The one wrinkle was that the relatives later shifted what they were joining us for, so trying to pick up more seats I used DM’s account to pick up an extra reservation for as many as I could at the closest available time. I set up alerts and then kept scooting things around until I got enough seats at roughly the same time.
At the time of our trip, I think we ended up having around 3 different meals where the reservations were split across 2 ADRs. We checked in in-person well ahead of time, told them we were willing to wait if needed, and for all of them they were able to seat us together pretty close to the reservation time.