Seems right now the low speed stability is a little out of touch. When you are coming into a tight corner, where you are basically at a stand still, its very easy to get off balance even with a stiff setup / inputs / rolling on the throttle. I've tried different variations of sensitivity and stiff setups to try and help combat this, some work better than others, but overall, the low speed stability needs a little improving.
Cornering:
Again, lots of different setup changes, and corning on flat ground is way better than trying to rail a well built corner. I dont think it has to do with the way the entrances to the corners are built, as i have done this on several different tracks. I've changed setups several times.
Example:
Built Corner (https://gyazo.com/5a38165415c68b91630ed4bfcb03e95f)
Flat Corner (https://gyazo.com/3096a0bdeb39564cb4bcf3ed7615362b)
Low speed stability is a known problem for many people as far as I know.
Regarding your examples, I don't see what's wrong. In the built corner you lean over too far which causes your handlebar to touch the ground, hence the falloff. Some of us have suggested 'drag physics' before. With this we mean that we can drag the handlebars on the ground without crashing, instead it should slow us down or change the handlebar's rotation.