Removing background using blend if

Hi

I've been asked by a friend to engrave a photo onto slate, but it's a collage of photos (mostly just faces) on a white background. I need to get rid of the white to make the background transparent ready for engraving.

I've searched for advice on how to do this and the answer I found (and tried was)

Create a duplicate layer

Use blend if (current layer) to get rid of the white.

This works very well but in places there are bits on the faces that it loses too.

I've tried using a black layer mask to get rid of these, but it doesn't work. See picture below for an example of what I mean.

When I apply the black layer mask, it starts with a fully transparent screen and I can paint on the faces that I want, but the bits on the faces are still transparent.

Am I doing it the wrong way, or is this the right way but I'm doing it wrong?

Thanks

Chris