Here now are more detailed photos of my School 34.
The School 34 lacks the small black rubber bladder at the low end of the A-34C’s reed chamber. I notice a slight difference in key responsiveness at the lower end of the A-34C (less responsive), which might be on account of the bladder and may result in a slightly richer sound at the low end of the A-34C. I leave it to more sophisticated players to comment on this issue.
A slight digression about “tools of the trade” here. Although there are better precision screwdriver sets, I’m liking this little inexpensive (about $5) set of Stanleys in the yellow box. These do not grip adequately and have too small handles for dealing with problem screws, for which you see the bigger supplementary drivers I have there. But once the initial loosening of screws has been done, these work well in repeatedly removing and replacing the reed chamber cover during tuning.