Not to keep you in suspense any longer, I made that block again, this time being a lot more careful about my quarter inch seams. And it worked!
It’s still a tiny bit smaller than it should be (I actually think my sewing machine is slightly out of alignment, because the needle doesn’t come down exactly central in the foot, but I’m not sure how to adjust it), but it’s close enough to 9 1/2 inches to be usable.
The difference between the two blocks doesn’t look like much, but it’ll make a huge difference to the final quilt.
An important lesson in accuracy!