i have done many reinstalls on my windows computer. to say that, just reinstall the games is best.
you are better off just restart from scratch to save all the headaches that may come trying to figure errors. its just a game installations...it's not like you're losing your game accounts.
This much I'm aware of...however from what I've read, the installer that's still within that folder is activate-able with origin to be able to re-install. To be honest, I don't know how it works but from what I've read, it seems viable...I guess.
its viable, the first priority would be to configure origin to autosave your games on the cloud, go to preferences and do it there, thats your safety measure.
the other measure you already did which is to get the save games manually, sometimes it requires for you to delete one or 2 files when you put, there a simple google search solves that
if you have 30gb + of free space yes you can try to install from within, it will give you an error, because the system is not upgradeable (you can move from 32bit to 64bit or vice versa), but it wil enable you before windows starts to install windows 64bit (you'll need a thumb drive) and thats it
you will have a windows.old folder on your C: directory, but everything from your old windows is going to be there.
or if that fails, my preference is just go into OSX, use the bootcamp app, remove the bootcamp partition, close the app, open it again, and install windows from there via a thumbdrive, simple and easy
gone is the time that this would be a difficult thing to accomplish