I know you said this doesn't work, but if I ever struggle with that, I look basically at their forehead between their eyebrows.
I never really had too much trouble with eye contact, so maybe this is why it works for me.
I only really have to do this when, for example someone has a lazy eye (Distracts me), or sometimes I get paranoid and I feel like I am giving them TOO MUCH contact, I start shifting from eye to eye not sure where to look so then I just look somewhere else.
People can't tell if you are looking at their eyebrows/forehead. I CAN tell when people look at my head (hair) and my chest, don't look down please.