Did you explain your situation to the Russian embassy? Theoretically, you could show up tomorrow and they could be sympathetic and for quite a large express fee you could get the visa on the same day. However, having already turned you away 4 times and Kazakhstan not being your official place of residence the chances of this happening are unfortunately extremely low. But this scenario would be the only way you would get into Russia.
Your only other option for getting out without flying, and this would be quite hard-pressed, is to head for Kyrgyzstan which has just gone visa-free for many nationalities.
Is there any way you can go to OVIR and get an emergency extension or something like that?
Lastly, if you know people and have somewhere to leave your car you could fly out and then fly back but I don't know if customs will notice that you've entered with the car but left without it.