I didn't see Rayny28's fix but I did the same thing. My only problem was it was trial and error finding the correct iPad 6.1 ipsw file. Mine finally worked wiith the one for the "older" iPad2.
Here is what I posted on another thread with the same problem:
I had the exact same problem and after much frustration and searching I found a solution that work. The only difference in my procedure is i see you have an iMac and I have a Windows machine but I think it will work the same once you determine the correct ipsw file to get.
I found this website that has all of the restore files for the iProducts which are lined to the Apple server that hosrs them:
:http://osxdaily.com/2010/11/02/download-ipad-firmware-ipsw/
Mine was trial and error because there were three different files for the iPad 2. but after the third I got it to work.
So what I did was download the file to my PC. Then I moved the file to:
\AppData\Roaming\Apple Computer\iTunes\iPod Software Updates on my laptop. For Windows users you will have to set the option to see hidden files. Not sure how it works on a Mac or what the location is.
Then I went through the restore procedure again in iTunes. After plugging the iPad in itunes told me I needed to do a restore. So I clicked on OK and then pressed (again for Windows machines) "shift" while clicking on the Restore button in iTunes. it will then ask you to find the ipsw file location. find the file and select it. If you downloaded the correct firmware version for your iPad for 6.1 then it should work. If not you'll get an error saying the firmware is not compatible in which case delete the ipsw file and download one of the others and start the restore procedure again.
On you get the right one and it starts to restore you can then restore your other apps and things through icloud. Good luck!