Might just need to ride it some more and get use to it.
After I got my 56cm Tarmac I thought the bars were too far out front, so I got a 70 mm stem to replace the 100 mm stem. First few rides were maybe what you call twitchy. Especially when doing downhill twisty paved trails and roads at speed or when encountering gusts. But a dozen or two rides and all that was in the past.
However, a few months later I also got narrower bars, went from 42 cm to 38 cm. And I swear the feeling of those same twisty turns and everything else became better than ever. Whether there is some math behind that I don't know.
Neither stem nor bars will do anything for riding no handed. But if your bars are 42 cm or wider, then narrower might make taking one hand off the bar easier for you. Narrower bars will also make your bike more responsive when you need to avoid sudden hazards in the road.