Alright I am going to share this weather I get chastised for it or not.

I have the same thing although I do not shave the upper lip (I have done it in the past) I clean it up and have the same type of hairs at the corners of my lip and at the top of my bottom lip.

The hairs are so fine they just bend away with the normal shaving angle.

I must be careful and pay due diligence but I hit them pushing perpendicular, as if I was doing the Coup de Maître right there in the open.

It kind of pins the fine ones down and makes them cut.

Be careful and go slow if you want to try this but it works well for me.