MB, this is an excellent idea. I share your sentiment re. getting a boring/weak/ nation or a nation that you down right don't like to play. Happened to me as well in this game, in the past RAND, and in the past past RAND
I sucked it up and did the best I can but I was anything but inspired.
Perhaps a semi random assignment system would work. Each player chooses 3 nations and conflicts are resolved by a die roll.