We all presume that Haman was well literate and familiar with our Tanachic sources. It is widely known that since the sin of the Spies (Meraglim) 9th of Av was chosen for all kinds of misfortunes for Am Israel.
I don't know if they observed the 9th of Av and the destruction of the latest Temple back in Persia, but the month was known for its bad luck.
On the other hand, as I recall, there were no bad events in Adar and Moses' death was albeit a "punishment" for Moses but not for the whole people that were about to enter the Promised Land with Yehoshua.
Why Haman didn't decide straight on the 9th of Av to complete the destruction of the Jewish nation?