John,
Sway bars and Spyders are almost the start of a religious war.... Chuck Beck generally takes the positon that a sway bar is a hinderence on a Spyder replica as he built them. And anybody who has ever ridden with Chuck in one of his Spyders will understand what he means. I have seen him entirely trash and beat badly, as walk away from "true sports cars" costing many many times the price of a Spyder, with far better performance technically speaking, all done without a sway bar. I suspect that in standard form without swaybar a Spyder will perform at about 90% of its true and full capacity. I also think that a skilled and experienced driver, such as Chuck, will beat me everytime, with or without a swaybar....so, if I were going to compete I would be taking a lot of driving courses and spending a lot of practice time on the track.
As to the sway bars, they will "help". But, be prepared to also add a z bar to the rear end, spend a lot of time testing, plan to change spring rates, shock absorbers, ride height, corner loading, tires, rim offset, alignement, etc etc etc.....I would recommend making the sway bar adjustable as there is no body of knowledge that says a good starting point is.....and what works well on a Speedster or VW bug or formula V, does not work well on a Spyder....I am aware of a couple of Spyders with substantial suspension "improvements". While they might be faster in a true out and out road race or autocross, my best improvement still lies in learning better driving skills and practice.
How close are you to where you want to be on autocross times, who is beating you, what are they driving, how much experience do they have versus you, are you spinning out frequently, or do you push on the corners, do you have LSD???? By the way, at least one guy I know says LSD helped his autocross times more than anything else he has done...