TL;DR: Fixed now. Thanks for spurring me to action.
Long version: I looked into uploading a new ImageJ 1.x manually, and discovered the problem:
ij-1.51n.jar was somehow erroneously uploaded to the Java-8 update site, so it was taking precedence over the newer versions of ImageJ 1.x which were successfully building and uploading to the core ImageJ update site.
I removed the
ij-1.51n.jar override from the Java-8 update site, and added this weird version (different than another build of 1.51n on the ImageJ update site!) to the ImageJ core update site’s history.
Hopefully, this will result in ImageJ 1.x being automatically updated from now on again, too.