Do you think I should perhaps replace Bayfiles with it?

I had originally intended to do something like this, but it looks like it won't happen at this point, with so much going on for me.
Maybe you could start up a blog perhaps? Or use an existing forum that doesn't mind this?

If not, I'm happy to simply install an existing script here (without much integration; provide suggestions if you wish), as you've been pretty helpful around here, but I don't think it would be any better than if you started one.

Thanks for the suggestion.
Does anyone have any anecdotal evidence of it working well?

I think Mediafire actually look at file contents - filenames are way too unreliable for this type of stuff.
Possible workarounds would be to encrypt/"compress" the file, but this means you have to extract it once you've downloaded it, and "previewing" the video won't work.

Thanks for the suggestion nonetheless.

1. MediaFire seems to be irreplaceable, for some reason.  I guess that's because it's almost universally fast and almost universally available.  Every other service produces good results in some part of the world and bad results in others, judging from the variety of comments.  MU was the only other service that produced relatively consistently good results world-wide.  I think therefore the focus of our discussion should be on getting MF, instead of alternates and mirrors.

2. I assume MF has noticed all the traffic coming from here and wants to begin making some money from it, hence our current situation.  Rather than ask admin to do any more than he already is, if someone else would be willing to maintain a premium account with MF and arrange for the AT bots to use that account?  I don't see any other real alternatives.  (Well, maybe one but I'd feel bad -tricking MF by randomizing submissions and user addresses.)

3. I worry that the charm of this hobby will fade for admin.

I'll see what I can do.