i’m crap on a bike, i’m a great example of ‘how not to do it’.
to my understanding, a bike feels stable because the front-wheel’s-contact-point is behind the steering axis.
this offset is called ‘trail’.
But as you lean a bike over and turn the bars, the contact point moves forward, the amount of trail is reduced.
try if for yourself; stand beside your bike, lean it over, and turn the bars into the ‘turn’ – look at what happens to the contact patch as you turn the bars.
i’m not sure how any of this helps, but there is a mechanical / geometry-related factor at work here.
A slacker head angle would help – to move the contact patch backwards, wider bars may help – to control the tuck, and stiffer forks – to hold the front end up – see head angle comment.
perhaps you just found the perfect amount of lean/turn to really do something weird to the contact patch…