I do like to use Klackons when playing Impossible (or Hardest in RotP). But I recently started experimenting with a new approach. I used to just try to build out my factories ASAP, to the appropriate population level. I usually build for 70% population, so 140 factories on the home world. And I'll do that on my second world as well, although sometimes I forget and it ends up with max factories.
But, I realized that on turn 1 Klackons generate more Research than Psilons. Of course the Pslion advantage grows as they build out factories. So, I instead switched to starting research right away with Klackons basically splitting my production between research and factories after I build scouts, and this has worked pretty well. It gives a good jump on research, especially for Construction and Planetology as needed. You can adjust Propulsion as needed depending on when you'll actually need the range.
But, I realized that on turn 1 Klackons generate more Research than Psilons. Of course the Pslion advantage grows as they build out factories. So, I instead switched to starting research right away with Klackons basically splitting my production between research and factories after I build scouts, and this has worked pretty well. It gives a good jump on research, especially for Construction and Planetology as needed. You can adjust Propulsion as needed depending on when you'll actually need the range.