I'm still at Monarch, but here's my $0.02:
There is a danger in specializing too much and not rounding out your skills.
You should not move up until you can clear the HOF and fill it with victories on completely random maps, except standard size. Tha includes random civs, and I like to uncheck the culturally-linked starting position. The only restart permissible is if you draw a civ you played in the last three games. Play until win or loss. If you loose - start over.
This strategy will gurantee that you have a good grasp of all the skills you will need to be consistent at the next level.