Let's take this in steps ...
First, make sure you process this raw file in 16-bit rather than the usual 8-bit. We'll need all that robust data.
Then do your BW conversion again, exactly as you've done.
Then add the overall Levels layer. You'll probably find that you can bring the white slider in to about 250. (DON'T bring the black slider in. Despite what you think, I don't believe there's any black clipping in this edit.) Then move the middle slider aggressively darker, I suggest to about 0.40.
At this point, you'll begin to recognise some of the characteristics of the other photo. Not all, but some. Enough for now.
Then return to the Background layer, duplicate it, then perform all your skin smoothing and blemish removal in the usual way.
Post for me once you've done that.