Windows 8 fails to load after Boot Repair

I've got a Sony Vaio laptop. Until yesterday I had Windows 7 and Ubuntu 12.04 (Precise Pangolin) installed. Today I upgraded to Windows 8, which killed my OS selection screen. So I booted to Ubuntu 12.10 from a USB stick and ran Boot Repair. This recovered the GRUB screen and let me boot into my Ubuntu 12.04 installation, but now I can' boot Windows 8.

When I select the option that booted Windows 7 before, it looks like it wants to start Windows 7 (sic) again (black screen with the text "Windows is loading" or something), but then reboots the machine after a few seconds.

I'm sure Boot Repair can fix this, but I know far too little about the whole booting thing to know the right settings for it.

Here's my Boot Repair report thingy: http://paste.ubuntu.com/1308117/

Update 1:

I managed to get back into Windows again. I changed the line

chainloader (${root})/EFI/Microsoft/Boot/bootmgfw.efi.bkp

in /etc/grub.d/25_custom (if you're reading this looking for help for the same problem: your file might be called something different) to

chainloader (${root})/EFI/Microsoft/Boot/bootmgfw.efi

and copied the file bootmgfw.efi from [Windows partition]/Windows/Boot/EFI to /boot/efi/EFI/Microsoft/Boot. (The file already existed, so I renamed it to bootmgfw.efi.old to back it up.) Lastly, I ran a sudo update-grub.

When I restarted the computer, Windows 8 was booting up again, but without a GRUB screen. So guess what.. I could not boot into Ubuntu now.

In Windows, I installed EasyBCD and added an Ubuntu boot option. When I tried to select that after another reboot, it failed because it couldn't find some file. I tried this with the EasyBCD option to find my Linux installation automatically, and I also tried manually selecting the partition. Both had the same result.

So I once again tried booting from my Ubuntu USB stick and running Boot Repair. This time I got Windows' OS selection screen (the one I set up in EasyBCD). When I selected Windows 8 there, it rebooted the computer.

How can I this fix this problem?

Update 2:

I can "switch" between Ubuntu and Windows 8 now. But not through a boot menu. (All the answers I've got so far didn't solve my specific problem.)

When I'm in Ubuntu and want to boot Windows 8, I do what I described in the first update (copy bootmgfw.efi from the Windows directory and change one line in /etc/gib.d/25_custom). Then Windows 8 starts without any boot menus.

When I'm in Windows 8 and want to boot Ubuntu, I start Ubuntu 12.10 from a USB stick and just run Boot-Repair. Then GRUB 1.99 starts and when I select Ubuntu, it works. (The Windows options don't work.)

So that's the current state – I can switch OSs, but it's a real pain.