Well for starters the Impala SS is a trim option (bucket seats and chrome) not a performance option. You could order an SS with a six cylinder in line motor (in 1962 that would have been the last year for the old 235 stove bolt six).
Good news is you have a stretch Corvette limo. The full size car frame and suspension (minus the length of the back seat) is sitting under a 1962 Corvette. The front half of that frame stayed the same right up until 1982, so a lot of Corvette front end parts interchange and are reproduced (even though the reproduction houses say no 1962 front end parts are available). Of course in 1963 the Sting Ray with independent rear suspension was introduced, so the back half of frame and suspension differs after that date. Though if you ever wanted to go the Full Monty (first definition "the full amount expected, desired, or possible", not the second as seen in Magic Mike), and swap out for IRS under the back you know where to look for parts. That is one source for fast power steering and disc brakes.
Bad news is unlike the First Gen 'vette that had two connecting rails to make a full perimeter frame along the out side of the X frame (similar to the Buick, Olds, and Pontiac X-frame cars) to stiffen the flimsy X-frame structure. Your full size Chevy was designed to float, flex and bend like limp noodle to absorb all road feel. It is mounted in sponge rubber to absorb any vibration and that rubber has long since rotted away and needs replacing (in case you wonder what that rattling noise is).
If you want a '62 SS sports car you need to stiffen the frame first with Polly body mounts replacing every rubber bushing you can find. Really want to go hard core swap out a BOP frame out of a 1958-'64.
Chevy was designed for the full frame with a X center, but outside rails were removed to cut cost. Note that BOP frames all used rear leaf springs instead of coils. Here is a Chevy illustration of the 348 powered 1958 Chevy Bel Air:
As to the 409 I would build a 481 instead. Using a 409 truck block and custom high compression hollow dome pistons (factory used heavy solid domes) to replace compression that the block cuts take away; add a cast iron 454 crank turned down to 409 standard bearing size. This yields a 481 displacement. I would also run Edelbrock heads and dual four intake, only painted Chevy Orange.