[joshvm]

Most commercial solutions solve this by using bright illumination from both sides to avoid shadows. In a pinch a couple of led under-cupboard light strips off would probably work. Something like:

https://www.interactive-education.co.uk/product/visualisers/...

It's almost always easier to control the illumination in the first place rather than fix it in post.

[HarryHirsch]

In the real world the "bright illumination from both sides" solution is called a makeup mirror. Just get one of those and glue the phone to it.