I found - as I moved up the difficulty levels - that I had smaller and smaller "windows" that I had to get through.
That is, on lower levels, I could colony rush for a while, over-extend a bit, and still recover, perhaps with treaties and playing off one AI against another.
On higher levels, I learned to be more disciplined when I stopped the colony rush so as not to over-extend, to focus my research on specific goals, and to get future enemies into early wars. The Drath, in particular, tend to get races to declare war on the human player, so it pays to get most of the galaxy at war with the Drath early. That means getting a diplomacy edge early, even if one cannot sustain it.
I found it important to get the early civ-wide bonus techs done and run to Trade simply for the economic capital, then not long after to Democracy to get the political capital. Those two help buy time in income terms.