Feel and twitchiness are very subjective - and most bikes , even ones with weird steering feel stable with practice (but its then other bikes that feel weird - maybe that explains how you get on with micro-bike ?). I find the most stable are 26" mountainbikes with big heavy tyres (ie guess this gives best giroscopic effect).
Again not sure about carry-me but i can ride a strida3 hands off, which is generally a sign of non-twitchy handling (I cant on a brompton). Older stridas, like you tried, seem to have no bearings for steering - I think they improved the handling on Strida3 with bearings and possibly improved geometry.