Updated: Mar 10, 2021
Bump your mower height up to 5" to 5 1/2". Mow it once. Lower it back down to desired height. Even though Kentucky Blue Grass likes to be cut at 3", you probably don't want to go lower than 3 1/2" since your grass is thick and already sits at 5 1/2". Wait one more week to drop down to 3".
Now mow your lines in the opposite direction. Not only will it look like you wanted the criss-cross or diamond pattern anyway, but now there's no left over mulch.
A lot of folks would kill for this lush, thick grass. I think your irrigation guy deserves a cookie!