I am currently running Koni adjustable shocks, H&R sport springs, and the factory "sport" rear sway bar. The front Konis are blown and are about to be replaced. Even before the Konis went south I found the ride to be pretty damn rough around town, where I do 99% of my driving. I am thinking of having the replacement shocks set to a softer setting than before, and adding either a 19 mm or 22 mm rear sway bar to help with cornering.

Is this a reasonable idea, and if so which sway bar would probably work the best? Thanks.

I would do the shocks first, and see how it handles. Take is to a skidpad if you can. Then do the rears if you need them.