Swapping the K-frame will work and is what I did on my '63 Dodge. Any K from a 63-65 v-8 car will work. They are all the same save for a few Hemi K's.
Depending on what look you are after and how racey the car will be, a motorplate might be a cheap, easy option. Knock the motor mount stands off the sland 6 K frame, bolt an AREngineeringplate to the front and weld a couple of tabs to the frame to secure it. We have a friend that did this with his street driven Dart and it does not have the vibration through the car that people say it does. Very neat setup.
There is also the option of a later B body k-frame, but that moves everything back 1 5/8", requires some tunnel work and mods to the transmission mount.
'63 Dodge 330
11.19 @ 121 mph
Pump gas, n/a, through the mufflers on street tires with 3.54's
10.69 @ 128mph with 150hp shot of nitrous