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A sway bar will have no effect on spring rate in straight line driving. A sway bar is only effective in resisting body lean in a turn. The rate of the sway bar is added to the rate of the spring only as the body leans.

 

I had similar ride quality problems with the Henry J. It has leaf springs . I'm already pretty hip to spring rates and tire pressure but I just couldn't get rid of the bouncy bouncy. While having a conversation with the late Bob Bauder (RIP) He brought up an interesting point. A Henry J is much like a Deuce roadster in that there is very little weight after the rear axle. He said he filled the rear push bar with lead on his car and it made all the difference in the world. I subsequently added a 1 1/4' thick 192# steel plate in the trunk under the carpet and bolted it down. I also added adjustable shocks. The car doesn't ride like a Cadillac but it's really good now !

 

What you're saying is the car was oversprung in the rear

That is basically "spring frequency" [ or cycles per second ]
It is like comparing an adult to a toddler on the same pogo stick. The more load the slower the frequency for the same spring stiffness.

Also the faster you go the stiffer the suspension needs to be. Drive around a race track at 20mph and you'll question the need for suspension, but at 100mph + and cars will bottom out.

Most builders use the "applied research and development" [lets try it and see] approach.
but if they actually corner weighed the cars and deducted the unsprung weight, they could actually get the project quite close first time.

A road car with 1400 lbs sprung weight in the rear, only needs 116 lbs/in springs per side [for a street cruiser]
Having springs this soft , usually requires them to be installed with a spring compressor as their static height will be quite tall. [with coils]