Steve - a "3 speed plus granny gear" is called a 4 speed around here
and a mid-60's 4 speed will be identical to a '58 4 speed - the trans will have no effect on top speed, they're all 1:1 high gear unless you find an overdrive trans, which will improve things - the other possibility is to change the rear gears to the 3.38 instead of the original 3.90, IF you have a 1/2T, but if you can't get over 60 with the 283 I'd guess you have a 3/4T with the 4.57 gearing
Bill
