The W123 can be predictable and neutral in handling and steering.

My coupe is an 83 300CD. There are minor weight differences but basically it is the same chassis and suspension as yours. The coupes have a shorter wheelbase than the sedans and should handle a little differently, meaning better.

You do not need springs. You need to get under the car and carefully inspect all of the suspension and steering components front and rear. Anything that moves in directions it shouldn't, any deteriorated rubber bushings and boots must be replaced. Remove and check your steering stabilizer.

Check your steering play. These cars have recirculating ball steering than can never be a crisp as rack and pinion. The MB spec is 1" or less of play at the steering wheel rim. DO NOT try to tighten it up with the adjustment bolt on the steering box. That is for another purpose. You will find that after you replace your steering bushings and joints, the steering play will be improved.

Replacing the shocks was a good starting point unless you bought some sort of JC Whitney junk. A surprising number of undercar stuff can be easily replaced DIY. After it is all done get an alignment and you should be good.

One more thing, tires. Bad tires can make the car feel terrible. If they are bald or mismatched replace them for your own safety.

This may seem a lot but you have a rare and desirable car that is worth some effort and investment. I promise you that tightening up all your old undercar stuff will reward you with a car that feels as though it is on rails. I also have a 2008 MB and my old coupe is the one I like best.