Normally the best chance to fill your freezer with cow elk meat is to hunt late season. There are many more cow tags available late and they are easy to draw in almost any unit.
It will be mostly residents hunting the late season, and most of those guys will not want to hunt far from the truck for a cow. Guys will go to the end of the earth for antlers but don't want to put much effort in shooting a meat cow. It will be crowded close to the roads, but over the ridge it will only be you and maybe a couple of locals out for the day on horseback. I have done this hunt many times and have done very well in filling the freezer.