My buddy has a 56 GMC Suburban Carrier with the stock 316 Pontiac engine and the original hydramatic transmission.
It also has the 3.90:1 rear end. That ratio is way too low for that truck, it is in 4th gear at about 32 MPH and sounds like it needs one more. First gear on the hydro is 3.82 which is lower than the stock 3 speed first gear at 2.94 and second gear on a SM420 at 3.58. If it was mine, I wouldn't hesitate for a minute to change to a higher ratio. Oldsmobile's, Pontiac's, and Cadillac's of that era used the same transmissions and they didn't use anywhere close to a 3.90 rear end.
Fred