As I mentioned yesterday, I got my stuff moved out of LGK (NPC Nullsec). I did this using the services of a third party: Black Frog.
Black Frog is the Nullsec / Lowsec service of Red Frog, which offers freighter service for Highsec. There is a third, called Blue Frog.
In the Link above you find a price calculator, which you must use if you want to use their services (highly recommended!).
So what's the deal? Why three different ones?
Black Frog: They move up to 320000 (or even 360000) m3 of freight, with a maximum collateral of 5 Billion. It won't get cheaper if you move less than 320000, so make sure you can fill a freighter. They operate in Nullsec and Lowsec and for a typical contract with the full collateral you pay around 150-180 Million ISK.
Red Frog: They operate in Highsec only, maximum collateral is 1 Billion. So, you most times won't be able to fill their maximum accepted size. But they are really cheap. With maximum collateral and 20 jumps you pay around 17 Million ISK.
Blue Frog: They are like Red Frog, but accept higher collateral for a higher price.
Black Frog already fulfilled my contracts, yesterday I found all my stuff sitting safely in Hisec. I immediately created 6 Red Frog contracts for letting it be moved to the closest Highsec system to my new Nullsec home. There are good chances that they already delivered when I come home today.
I absolutely recommend their services. Don't transport your stuff yourself. Use those guys. Seriously!
It's riskfree for reasonable prices. Let the pro's do the hauling ;)