For good measure, DO look to see what everything is in the front end. With age, the rubber bushings will "settle out" as they age with the weight of the car on them. The upper control arm bushings AND the pivot bushing in the lower control arm. If there are some "weather cracks", that's about normal, but if there are any missing "chunks", that's cause for concern.
Your "over-sensitivity" could be the higher level of boost the earlier cars generally had, or it might be the toe-in adjustment a little out of spec, such that when one wheel gets on a different surface, if it's a gripper surface, the car heads in that direction.
Those Chryslers were sometimes "a target" for front end mechanics, as many lower ball joints were replaced when they were "in spec" and NOT worn. There is a spec for their "looseness", that's normal in the manner it is checked.
The steering adjustment can be a little loose, too, but adjust that sparingly. There are two adjustments, one on the input side (forward of the rag joint) and the one on top that everybody knows about. But with the mileage your can has, the box is far from worn out, typically. But "a touch" more on the center adjusting stud might not hurt, but if the return of the steering wheel from a turn doesn't happen, then it's too tight. In many cases, it's the input-side adjustment that needs attention instead. Note if when you turn the wheel from side-to-side (from center), the steering column (at the gear input) moves in and out before the steering gear moves the steering linkage. The "spanner nut" adjustment, I believe, it's called.
AND, it could also be the brand of tires and their tread design! Make sure the front tires are also inflated to 30-32psi cold, for good measure.
In the mean time, get it all checked-out and see what it's "made of". A few quirks you can PM me about.
Enjoy!
CBODY67