As well as the two points of mine you dismissed on this front, there is the larger-scale consequence that the red Court ends up seriously weakened, which also works for me.
He didn't start it; Grevane started it. Cowl was hiding and invisible until after Harry had disposed of Grevane. What do you think Cowl would have done there if Harry had not turned up at the right time ?
The athame places Cowl firmly in the outsider camp most probably as their tool. Introducing Nemesis into the Sidhe Courts is simply too big for someone who merely uses the outsiders for his own purposes.
The outsiders want to weaken the Sidhe courts and most probably the white council as well. One of the functions of the seven laws is to keep the outsiders out and a side effect of the hunt for warlocks is the reduction of the number of potential outsider summoners.
There is no reason for Cowl to flush out Grevaine and Corpstaker, they are no hindrance for his plans except as competition for exactly what was happening, the darkhallow.
There was no reason for him to weaken the red court, the red court was his tool against the council and was probably intended as a tool against the winter court later. It had enough enemies so weakening was not an issue, strengthening was and the darkhallow would have been an ideal tool for that.
There was of course reason for Cowl to stirr the red court up but they were doing that fine already and a successful darkhallow followed by the destruction of the senior council would have done that job quite well.
So Cowl did the heavy lifting for the darkhallow while Grevane and Corpstaker were trying to kill each other. He took Bob and freed the erlking so his spirits could have been consumed as well. He helped to get the darkhallow forward and at the end he started taking power, that was the moment Harry started his dead curse and everything spiraled out of hand.
So weakening the red court was not an issue. If anything he wanted them stronger because the Winter court was still far stronger than the red court.
Flushing out Grevaine and Corpstaker was no issue because they were only a problem for the white council, not for him. Unless he wanted the darkhallow because then they would be competition but then the flushing out would be a side effect and not the purpose.
Making Harry think he was dead was no issue either. He was wearing a disguise so it was just simpler to drop it and assume another one if he wanted to disappear without anyone being any wiser.
Getting power was an issue. It would help him with whatever purpose he had and the side effects were not important anyway when the gates were broken.