If it's going to be possible (and I'm deeply skeptical) there can't be those black shadows. Start again with your raw processing, without ANY black clipping.
I think to be safe, you'd better replace the background, either with a flat light grey that matches the background nearest the baby, or with a gradient layer.
Comparisons to other computers are irrelevant. The only comparison that matters is to your pro lab prints. Describe that to me. How does your screen differ from the prints?