If you shorten the rear frame section the 12" it should work fine. It will be very close to what a short bed truck was, so geometry shouldn't be affected. Might even check the driveline/wheelbase of a similar shortbed first, and see if it's close enough, then cut to that length so you could use a actory driveline from a junkyard.
As John Se mentioned, you'll want to cut the frame the needed length, then plate over the area after welding it back together. I would also box the inside for about 12"-24", just for a bit of extra strength.