Ok, so I've made a little progress now. I hooked my iPhone up to other computer with a freshly installed copy of iTunes and it recognized the phone was in recovery mode so it's downloading the iOS 5.0.1 update and going to restore to factory defaults.
I've got about 15 minutes left on the iOS download so I'll post again once I see how that turns out.
The restore on my second computer worked and I was able to sync the phone with my main computer to get everything back on it.
So, for anybody that runs into the same issue here's the steps I took to fix it.
1. Install iTunes on a different computer
2. Plug in the iPhone to the secondary computer
3. Perform a factory default restore
4. Unplug the phone from the secondary computer without setting up the iPhone.
5. Plug the iPhone into the main computer
6. It should ask if you want to restore from a backup
7. Wait for the sync to finish.
Not entirely sure what went wrong to begin with but I did send off the crash report to Apple when it asked so hopefully they can fix it.
Thanks to the two responders that tried to help but luckily I had a spare computer to work with!