The 1957 Chevrolet Truck Engineering Features book talks about the "new" 98" pickup box for the 3204 and 3604 models. If the assumption is Chevrolet used the 89" box on early 1957 models (to use up inventory) than they would have needed to use the 1956 frame as well (which is 8" shorter than the '57 frame).
Just curious, what year is stamped on your 1957 short frame as part of the serial number? It's found on the top of the frame above the front axle, drivers side.
So to answer your original question, you will need to add frame extensions to the short frame in order to bolt the rear bumper on and transfer any bed mount holes for the longer bed to the shorter frame.