I have this exact same problem you describe in the original post. I posted here
http://forums.amd.com/game/messageview.cfm?catid=405&threadid=150533&enterthread=y
I could get any combination of 3 or 4 monitors to work, just never all 6. I had a diamond 5870 eyefinity edition at first , then i got a an asus 6970 that works with eyefinity 6 here:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121430
I reinstalled windows 7-64 with the new card and still had same problem.
I tried about 12 different cables from monoprice as well as cables that came with the monitors themselves and nothing worked.
I don't know if its a cable problem or a problem with displayports on these NEC monitors.
The only way I could get all 6 to work was to buy all sapphire active displayport to dvi adapters and use only dvi cables. It worked first try after that. It defeats the purpose of having a displayport capable monitor but its the only way I could get it to work.
Do you think it would work with only 4 of the sapphire active mini-displayport to dvi adapters? Yes, there may be a problem with the NEC monitors, but after a call to NEC they tell me that it is not an issue if all 6 monitors can be displayed (w/o Eyefinity). I think the Eyefinity tech has not been fully developed yet.