I'm practicing this on Emperor. It seems my biggest problem is that my archers take so damn long to build. I reach construction before I've had a chance to build all my archers. Especially in my 2nd city and 3rd city, it takes forever to build he archers.
I had the same issue on epic speed. Just tech elsewhere in the tree until you are satisfied that you archers will be finished and then tech Construction. At my slow paced games, I tech to Philosophy then swing back to Construction.