Starspiker :
I'm saying that the folder the games are in, D:\Steam2\steamap\common, is that I have the library set to, but Steam fails to recognize that they're there
Unless you made a typo: the directory should be "steamapps" not "steamap". Try that first.
There is a very good chance that to get the games to appear on Steam, all you have to do is go to the game as listed in your library, click install, and choose the library that is on your D drive (specifically, pick the Steam2 folder). Steam will then recognize that the game was already installed there, and will verify the game files already there and download whatever is missing or any updates.
At least, this is how I get my externally stored games to be re-added to Steam. So considering you are having the same problem I had, this could do it.