I just discovered something in further testing (and figured out why my initial attempt to reproduce it didn't show the issue)! It is something about the Views themselves that we have (in both "his" Library and my own) that causes it.
On both of our Libraries, I can reproduce it when drag-dropping Views within in the Audio section of the tree, and those within the Advanced (All Media) top-level Views I made. But, if I switch to Video or Images top-level Views, and drag-drop within those, it works correctly. No hang, and the drop-target works properly. I just checked, and the same thing applies to my copy of MC 26 on my Mac Mini (which has it's own "version" of the local Library, though much older).
When I first tried to reproduce it (before I'd started recording, as a "sanity check") and then couldn't reproduce it, I was in the Video views (because that's where it happened to start up when I launched it).
I should also briefly explain about the "local" Libraries on these various machines: I don't really use them. These copies of MC are used effectively exclusively as Clients. When I install MC, I do set them up with local libraries so that if I need to use MC offline with local content, I have a working option. To do this, I take a current backup of my main server's Library (a snapshot of it at that moment), and restore it to the client machine. Then I go in my Advanced\All Databases View and find-select all of the files in the Library and remove them until there's nothing left. Then, I import any local content I have stored on the machine in question. The Laptop in particular, because I was just getting MC27 set up on it, was in a bit of a state of dis-repair for this reason (I hadn't really finished setting it up yet).
The Mac Mini hasn't been upgraded to MC27 yet, and so it just has the Local Library I set up (as described above) a year or 18 months ago or so when I set up MC26 on that machine. But, same deal on it. I can reproduce it in Audio and Advanced/All, but I can't reproduce it under Video or Images (even though the "version" of that Library I have is quite old).
However, I "cleared" the "default" Library on my laptop's MC 27 copy and I cannot reproduce it there, but it is still happening on my "Laptop" local Library and my brother-in-law's (and my Mini's Local Library). So, it seems to be something "within" the Audio and/or Advanced top-level Views I have in all of those.
The thing is, I did not restore my Library on-top of my brother-in-law's machine (via that method I described above). I was recreating a number of the same Views I have in my own Library for him, but I was doing them by hand, because he has his own content I don't want to clear (and he doesn't need exactly what I have and use, he needs some of it, tuned for how he's going to use it).
I should also note: Windows doesn't have any issue with any of these Libraries. In fact, that's how I got past my issue with my brother-in-law's system. I restored his backup onto my Windows machine, made the changes there, and then restored it back to his own machine. So, whatever it is, the Windows version of MC is immune to it.