It seems as if WP has a problem with pinging the particular sites I am linking to (mostly pages on Westlaw which require authentication). If I link to https://www.espn.com or https://www.amazon.com (which other users reported having similar problems with before 1.5.2), for example, it works just fine. Therefore, I think the recent revision of post.php solved the problem partially, but not all the way.
I replaced my post.php with the version you linked to and it still hangs… It’s gotta be WP, since the posts without links publish and update just fine. Any other ideas? Is there an easy way to just disable the pinging altogether?