I am thinking of doing a road trip to Georgia, dumping my car there then travelling to Moscow, to continue on the Trans-Siberian to Beijing. Does anyone know if its possible for me to travel over the border either via coach or train or should I re-think my plans?
As I've said in this answer, you can use Baku as connection point, and use train to travel. There is no such problems on the border between Azerbaijan and Russia, and you wouldn't spend much time on this trip.
Another option is to get into the Abkhazia from Georgia (if you can), and use the train to the Moscow. But in this case you'll get problems with Georgia officials at the next visit into the Georgia.
As you can see in this question, the biggest problem is probably that the border is sometimes closed for non-citizens. So you have the problem that it is not always possible to enter Russia from Georgia.
As you can see here, there isn't a direct train to Russia anymore. But you could use a coach or the ferry.