A professional British car specialist here, Mike Gassman of Gassman Automotive, informed me that with <span style="text-decoration: underline">stock</span> front suspension components, a 3/4 sway bar is a bit too much for a STOCK Midget front suspension. It makes sense, really.
The sway bar is bolted directly to the spring pans thus it takes a LOT of stress from the suspension travel. Increasing the diameter/size of the sway bar introduces a significant stressor to the system, and would not seem a great mod from a safety standpoint, IMHO. The added rigidity that the 3/4 bar gives may be a bit too much for the OEM suspension setup, as noted in posts above.
Mind that I'm referring to a stock, MK III Midget here, but the physics are similar to the Bugeye setup. Unless you have upgraded, stronger suspension components, go with the smaller, stock sway bar.
FWIW, I went with a totally stock suspension rebuid on my Midget and couldn't be happer with it. After completely rebuilding the entire suspension on the car with stock parts (all parts from Moss except the steering rack), I was very pleasantly surprised at the handling and ride of this car. Nice, smooth ride with little body roll and really great handling.
Stick with stock parts, unless you're upgrading the major components: that's what the car was designed for.