Disclaimer: I don't have an S3 (hopefully, yet). But I do have a Galaxy Nexus.

I used MyPhoneExplorer (MPE) to backup/transfer my contacts, call logs and sms from my SE Xperia Arc to my Galaxy Nexus. For apps, I didn't bother as I just reinstalled manually, to avoid any incompatibility with ICS. For specific app data like Whatsapp data, I never bothered as well, as I use Whatsapp for purely non-work related stuff. However, having said that, I think you can backup and restore apps as well with MPE.

You will need to install an app/client in your phone as well as a program on your PC. For info, visit here: www.fjsoft.at/ If you are facing any problems, have a read of their forums. Good troubleshooting resource.

If there are no problems, this way is pretty convenient to use. You can use MPE to make periodic backups and to sync with your MS Outlook and other similar clients too.

All the best. Cheers.

What about trying going into "Flight Mode" first, then coming out of it?