As you said, I think the GW problem is the biggest issue.
The fuel burn during climb out would definately be brutal. And it would probably need a couple of JATO bottles and using Groom Lake in winter to get off the ground.
I suspect it would also need some kind of dolly, which would fall off at take off, because I doubt the landing gear would support that much weight (or the rolling resistance would be way to high at that weight).
I did find some other specs for the 747-400ER, which also improved on your numbers, but it wasn't clear to me under what conditions those numbers were valid, so I didn't quibble with your numbers. For instance, I found a specs on the Boeing website of over 7000 nautical miles, a cargo weight of just under 200,000 lbs with a gross weight of almost 1,000,000 lbs for the 747-400ER.
So a 747-400ER can do almost 8000 statute miles and the cargo weight is about twice your estimate, so I'm getting close, but I'd still have to load it well above spec.