Do you use PowerArchiver (PA)?
Here's a recent thread were one of the admins says about sharpshell and PA:
it is a backup bug, it doesnt have anything to do with icons in any way, it is just that backup writes wrong values in PA registry once completed and causes issues…
Even if you don't use PA; Is FreeCommander similar? It may still be a clue to what's going on. Maybe Box has the same problem with sharpshell and Box's registry. You've already touched on that in your
#7 post.
I agree with your assumption that:
Obviously something was updated or changed,
Being that sharpshell and possibly Box works with .net, have you tried repairing your .net versions? I don't remember if repairing was suggested earlier or not.
Go to:
Control Panel\All Control Panel Items\Programs and Features, let it populate then look for .net framework >left click on the entry [if more than one do each separately] >click on uninstall/change >make sure the
repair radio button is selected and click on next and follow the prompts to finish.
The initial screen does say: repair to its original state, so you may want to consider a windows update check, I never did a check thinking that windows would catch-up during the next monthly update, in the mean time it fixed a problem that I had and it never came back. At one time I had several .net entries back to v2.0 but over the years microsoft consolidated them all to v4.6.1 .
In case you see an error that the native repair can not continue because the installer (MSI) is missing or corrupt [that could be the cause of your problem] try this:
Introducing the Microsoft .NET Framework Repair Tool/.net blog
Make sure you click on the download center link shown in the "get the latest version section", the blog states that the tool goes up to v4.5.1 but the details section at the download page has a note that it is revised to work on v4.6.1 back to v2.0 SP1 . Related:
.NET Framework Versions and Dependencies
I looked around and Box is one of few storage solutions that offer free/10GB/250MB upload, the only other that offers greater is
google drive at 15GB free,
upload limits vary.
Some users hate google because of its ubiquity and privacy concerns but I use gmail and I've set the privacy controls to max, they've been running HTTPS for 12years now and
gmail's been encrypted since 2010, we've been using gmail since 2004 and the only problem, if you can call it a problem was the other day when my wife started up her new laptop and signed-in to her gmail, we both received an email notifying us if we recognize the new sign-in, all we had to do is click on yes, it's OK, and that was that.
I could go on and make this
tl;dnr 
so if you have any questions about google drive just ask.