I have reasons to believe that this works for LG E900 Optimus 7 phones. If you want to try this on your Samsung Omnia 7, please read my note at the end of the post.
Here's what I did (LG E900 Optimus 7 / Windows 7 64bit):
During Step 6 (Rebooting your phone), your Windows OS detects your phone as a new device and starts searching for driver updates online. This can be seen when you click on the little indicator with a spinning green circle in the bottom-right corner of your desktop called the notification area (you might need to click on Show Hidden Icons if it's hidden).
You have to *immediately* click on "Skip Obtaining Device Software Online" or Zune will time-out and show error 801812C1.
Once you've skipped obtaining the drivers online, in about 20 seconds or so, your device will be recognized and you will be promptly taken to the Step 7 of the update.
Note for Samsung Omnia 7 users:
Even if you've gotten past the Step 6 801812C1 error, many users are getting stuck at Step 7 at 100% of 'Backing up your phone' resulting in a few users getting their phones bricked -- you might want to wait till that issue is resolved before trying this fix.
Hope this helps.