Judging from what you've said, I'm 99.9% sure that this isn't a Reaper specific problem. I'm pretty sure that your Windows installation is jacked up- Reaper itself only uses what is properly installed on Windows, and makes no changes to the OS.
My suggestion:
- Do not uninstall Reaper.
- Uninstall all the drivers you've installed for your Soundcraft.
- Uninstall ASIO4All.
- Download a copy of CCleaner from Piriform and go to the Registry Tools and have it "fix" all the registry items on your machine.
- Download a fresh copy of the Soundcraft drivers and make sure that if there is an option for an x64 version of the driver that you use that one.
- Open Reaper and see if it sees your driver now.
If the driver registers itself properly, you shouldn't need ASIO4All at all.