So it's an officially unlocked model? You don't rely on any software unlock?
Then go ahead and restore with official 3.1.
In this special case there is no advantage in using any specific iPhone OS.

But since this phone has been seriously tampered with obviously, I wouldn't even trust the model number. I don't think you can get the phone part running again, cause you would need an IMEI for that. And depending on where you live, obtaining a new IMEI could be illegal.
Anyways, I think you're even out of luck flashing the baseband to begin with. Since you don't have any radio service running there must be something wrong with the CommBoard. But, trying doesn't hurt, does it :-)
Good luck!