My neighbours were thinking of importing a car from Germany, it sounded really simple. Could it be anything to do with where it is coming from ie easier from Germany than the UK, rather than who is doing it? Do Germans resident in Greece have the same problem if they want to bring their car over? It might be that in buying a new car from Germany the first registration will be as a Greek car so all the hassle doesn't apply.
As you can see I can't help much. I certainly don't know anything about extending the six months.
The only thing I can say is be careful. If you "sell" your girlfriend the car and then split up, (sorry not implying anything, these things happen) will you get your car back?