Working on that very thing with my overly large kart right now, never mind that it has full A-arm long travel front suspension. Comparison on the steering works out the same.
Homemade rack and pinion steering to get 320 degrees of steering wheel had to be cut off, started over, ended up making a pitman arm setup like average karts, with the usual 10" steering wheel bought for leg clearance. A pitman arm limits steering wheel to about 150 degrees max, and coupled with a little 10" steering wheel makes a very twitchy setup.
Because my steering shaft ended up several inches too high to make a direct pitman hookup, I put a sprocket on the end of it, and a sprocket on the pitman's pivot point, hooked up a chain around it with a solid tensioner. Here's the difference..............
I used a 13-tooth on the steering shaft and a 32-tooth on the pitman arm. Hoped it would give me a lot more steering wheel, and it did help but still fell short of what I really wanted, the math looked right but didn't apply right. Point to you is that the sprocket differential and the 13" steering wheel I'm ordering are both answers toward your goal of less twitch. Pitman arms and rack-and-pinions come equipped with fixed limitations you can't change, as does a tiny steering wheel. The sprockets and the wheel size are things that aren't fixed, you can do plenty of things with that.
NOTE: Doing a center-drive/left-drive convertible setup. Will chain-drive the left to the center, where steering shaft will remain, only steering wheel will swap around. Will do another sprocket differential there, much greater. Left-drive should get about 540 degrees of steering wheel.