How do I add replay files that're saved from toribash to the toribash folder?

The easiest way to do that is to drag the replay file to your toribash replays folder.
(The toribash replay folder is located in: My Computer<Local Disk<Games<Toribash<'replay'.)

I can't drag files from the application to, well, anywhere...

The ones in the application are already saved in the replay folder

No, they aren't in my replay folder anywhere.

If you can find them on the toribash application, then they're in the replay folder, make sure when you're looking you're not filtering out any other ones. I believe they're saved as .rpl

The only replays in the folder are the default replays (whatever they place there when you download the game).

Huh... well I doubt the game is saving them some place else, so maybe you're not saving them correctly in game, and if you still are having problems, might I suggest you turn on autosave? You can find the folder for that, in the same place replays are. So if worst comes to worst, you can just find the replay's in there, change the name, and drag them into you replay folder.

There's nothing in the autosave folder ._.