I came across this exact problem. I am using NTSC-J wii 4.3.
To load spec ops and multiplayer, you need "Force PAL60" (I use USB Loader GX).
To get the update, you need to modify you shopping country code to be the same with your game (US). I did it like this:
1. Open shopping channel, delete the account data. You will need the serial number written on your wii. Note that your wii points there will be lost.
2. Use AnyRegion Changer 1.1b, load it in Homebrew, only change the shop country code to 49 (US). (Becareful not do anything else it may brick your wii)
3. Open shopping channel again, this time it will be in English, agree to the terms, open it again and you will see the US shop.
4. Now open MW3 multiplayer and get online, it will prompt an update and download it. You are all set
If your MW3 is PAL, change shop country code to 110 (UK).
After updating the game, you can also change the shop country code back and use the JP shop again.