Welcome to the forum.
The 53 Buick was a tank, as all Buicks were. Handling was not in GM's mind when they were built. Ride quality , was important.
In 53 the auto industry was changing rapidly. Many cars used shocks that resembled a hydraulic door closer. The Buick also had a "torque tube" instead of a conventional driveshaft.
Automatic transmissions were just becoming available. The Dynaflo was one of the early entries in that idea.
My point being, a frame swap, clip or other major operation , could be an improvement. But it is very time consuming, and may or may not yield a car that has the characteristics that you want.
Some type of Disc brake conversion would be nice, because it's had to stop a 5000 lb. car.
I dont think you can improve on the handling without destroying the ride, but you can make it safer and more reliable.
"The oil goes round and round and the power comes out here" DynaFlo