It is my opinion that you will gain more DPS by using your DOTs early, even before Dark Evangelism and Empowered Shadows go up, when starting a fight. Since Dark Evangelism and Empowered Shadows should be up by the next time you need to reapply your DOTs, this leaves the window of variation between using them earlier or waiting quite small. Also, I don't like the idea of casting your DOTs, then reapplying them immediately after you gain your Dark Evangelism stacks and Empowered Shadows. I feel it would be better to just wait for their normal reapplication.
These are assumptions based on logic, and while I have seen the idea you proposed by other people, I have yet to see someone present a conclusive answer on the best way to open. However, I have requested it. I think the idea is that most people don't want to put in the time to figure out whats the best way to DPS over a span of ~12 seconds (I could be wrong). I still look forward to an answer though. For now, I'll stick with what seems to make sense, as well as follow what simcraft codes as its priority action list.