I know of only one way that this can happen in windows, and has nothing to do with Steam other than their not-so-great decision to install all content into Program Files.
If you are on Windows 7 or Windows Vista, and you have UAC set to ON, then change it later to OFF, this can happen.
UAC does thing evil thing where if a program tries to write to a "protected" area like Program Files, EVEN IF YOU ARE ADMINISTRATOR, when you get a UAC prompt and give permission, it actually writes any files that would normally go into that directory into a "virtualized" directory somewhere else.
If you turn off UAC, that will no longer happen, and as an awesome bonus, it will no longer know about the files that it virtualized.
So in your case, if you had UAC on, installed a ton of games, then later got sick of UAC and turned it off, this would happen as you described.
See the second paragraph in "Features" in the article on User Account Control.
If you have done this and turn on UAC again, your content will come back, but be a TOTAL mess because if you've downloaded more stuff with UAC off, then that will be invisible when you turn UAC on, and vice versa.
this drove me a little crazy once before I realized what was happening.
i'm curious to know if this is your issue.
I also start Battlefield 3 through Steam, so that I have the overlay and friends can see what I'm playing. I never had the issues you're reporting here.
But: How do you start Battlefield 3 from Steam? The shortcut I created links to the Origin.exe, otherwise it didn't work for me. Maybe you link to the battlefield3.exe?
If yes, try linking it to Origin, I've never had problems this way.
Best Answer
I found those instructions to disable Borderlands 2 (I don't know if Factorio) from synchronizing save data with Steam Cloud here:
I imagine you already tried that, but it's all I found. If there's no other solution that's a pain in the ass, I assume save time will get even longer as your map keeps expanding, so I guess Steam will fix that for you if you ask, since it's their fault you can't really enjoy such a great game.
Good luck!