After more than 3 hours I accepted the first ride that took me somewhere between Lakselv and Karasjok. Don't be like me! Only accept rides to at least Karasjok. There is nothing in between.
After 2 more hours in the middle of nowhere I hitched a ride back north, and took the route Alta->Kautokeino->Finland
Disclaimer: it was a sunday, so you might be more lucky on a weekday.