Integrating a dash cam into your car is doable. I used to have a GPS antenna at the top of my windscreen, wedged between the roof lining and the mirror mount. The wire ran along the edge of the roof lining, inside the A-pillar trim and through the dashboard to a power supply I'd placed in the center console behind the stereo.
You could attach the camera to the rear-view mirror (fabricate a bracket that attaches to the mirror mount). Check if you can wedge the cable between the roof lining and the window.
If you want to run the cable behind the A-pillar trim, check if there's an airbag in there first.
This requires a bit of work and some tools (removing trim panels becomes a lot easier if you have the right tools), but an amateur like me can do it in a day.