"Based on the above, that equates to 0.7 disabled children per school and 0.1 trans children per school."
This is why I think y'all are over reacting a little on the transgender kids 'taking over' disabled toilets.
At many schools there are disabled accessible toilets and NO disabled kids. They're built in advance in preparation for when a disabled kid does come through the school but are not actually needed regularly for their intended use. On your statistics a bit over half of all schools have a kid with a significant disability.
At large schools which have many disabled kids there would likely be several accessible toilets (and if not, we need to build them!)
There are more and more kids identifying as queer, non-binary, or neutral, but the number who are identifying as transgender to the extent that they demand access to seperate facilities remains pretty small, so small that only 1 in 10 schools has even one student.
In schools where there aren't disabled kids, or where there are plenty of disabled accessible facilities, is there really harm in allowing the transgender child to use them too?
In cases where there are many transgender kids and few facilities, such that allowing those kids to use the disabled stall is likely to disadvantage kids with genuine disabilities, other options could be made available for the trans kids, i.e. the staff toilet or a portable toilet could be hired temporarily until an extra stall can be built.
Obviously the needs of the kids those facilities are built for (girls, and disabled kids) should be prioritized, but at the same time you could for example allow a transgender student to use the girls change rooms AFTER the girls have left without compromising anyone's rights. You could let them use a disabled neutral stall AFTER the kid with a genuine disability is finished without harm too. Or use the other disabled neutral stall on a campus which has more than one toilet block.
Long term we should build additional sex neutral single stalls but I think this whole transgender thing is going to be a passing fad that a decade from now will seem ridiculous, so we should make them accessible too so that they will still be useful. So that still means you would have transkids using disabled/neutral accessible stalls just that there would be more of them.