For everyone saying MD season in October will ruin November elk hunting, I assume your mechanism is bumping elk while hunting deer. I guess I don't see that happening for a couple reasons, depending on the area.
1. Elk and mule deer have different habitat preferences. If you are hunting bucks in the first 15-20 days of October, they are going to be in different areas entirely than the majority of elk. As bulls pull off the cows, bulls and bucks may show more overlap, but still will not show much overlap as bucks move into the pre-rut and bulls move into their post rut hell holes
2. Direct vs indirect pressure makes a huge difference, ie getting shot at vs not.
3. Neighboring states that run similar season dates don't see the mass migration to private of elk, outside of areas without much public land, ie NE Wyoming.
I don't think you can get more elk moving to private than you already do with 12 weeks of straight hunting with a 5 day break at the midpoint plus multiple months of shoulder season on either side.