We've beat this old horse a number of times so here's my two cents...once again.
The 356's handled really well considering the years they were in production. Compared to a Buick they were race cars.
A properly set up replica can be made to handle just as well as the original cars.
I've owned a 356 coupe, built a replica and have one of them store bought replicas today. The key is properly set up. These cars were designed around the VW design. There were a number of VW parts on the 356's from the factory.
The 1600's were 60hp cars; 1600S, 75hp, 1600 S90, 90hp. All 356's came with an anti-sway bar on the front. They did not come with camber compensators for the rear, but Porsche offered a kit that was different from any on the market now, but similar to the EMPI product. The ends of the spring could be preloaded and Porsche had a recommendation for that.
You will want the sway bar and compensator on your car. Additionally 356's carried a spare tire, jack and tool kit in the front; about 40 pounds. The handling is seriously adversely affected if that weight is not there. I suspect that most of us don't carry that equipment. I added about 26 pounds of steel to my front axle beam to take care of that.
Put your mind back in the 1960's; you can throw a properly set up swing axle car around the corners.