Wally, I would suspect a swaybar would help with front end grip, specifically it should help reduce front end plough and terminal understeer at the extreme. You might need to go to a thicker front bar also to maintain balance as I believe too large a rear bar with a smaller front bar can make it a bit twitchy, but it certainly would be worth a shot. I don't know if Herb Adams is still making suspension bits ( I forget the name of his company) but I know he was a great believer in the use of sway bars (or anti-roll bars) to control a car through the twisties. If you can find his company he would certainly be able to help with any tech problems.
The only thing I would be worried about would be torsional rigidity in a convertible compared to a hardtop, and whether or not the structure would be under much more stress. I guess it depends on just how fast you go through the chicanes.
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