This is a bad recommendation for the OP's purpose. Tannöd is written from the perspective of the inhabitants of a rural Bavarian village and would do quite the opposite than let the OP's German sound less 'proletarish', it could get even worse when she picks up the Bavarian coloring of the narrators.

I would recommend Elisabeth Herrmann - Zeugin der Toten.

http://www.ullsteinbuchverlage.de/li...07&page=buchaz

It's about a former drug addict who comes across a murder case with strong ties to her childhood in an orphanage in the former GDR. Although the story runs along the activities of diverse intelligence agencies, it's suitable for crime readers who don't like spy thrillers.