Jmoat's solution solved the exact issue we were facing with our new iPad mini's.
Two notes: 1) We had to walk through the enabling the options on the ipad with it still connected for the .ipsw file to appear.
2) We copied the file into our Documents folder using terminal since the Library folder was hidden using the command like cp /Users/USER/Library/iTunes/iPad Software Updates/*.ipsw /Users/USER/Documents
Thanks for documenting your troubles to help others!
Botanical Research Institute of Texas