No-Fork project, bicycle geometry hacked

I'm no engineer... but wouldn't there be a problem with the OP bike when taking sharp left hand corners quickly? What I mean is; there's only so far you can lean over, and this design reduces that (when turning left) by the amount the wheel is pre-leaning.

No (approximately). The lean limit is when the plane through your centre of mass and ground contact points is at about 45 degrees to the ground; your tyres start to slip out from under you as you ask for more sideways force than the static friction of the tyre contact patches can provide. That plane doesn't change just from fitting wheels in a different plane - leaning just the wheels doesn't change the sideways force demanded of them.

('Approximately' because the tyre's friction properties may change as you run if further off centre - probably different surface material and pattern, and also they may squirm more when rolling at a funny angle.)

The other limit is if you get too large an angle between centre of mass lean plane and the plane of your wheels: then they may collapse. But the OP's wheels seem to be dished to cope with their offset.