Fred,
As always, great post!
I have tried a number of ways of hunting elk in Montana. They've ranged from cow-calling during bow-season in September to waiting until the poor things are driven downhill by snow and cold in late November. Both tend to involve knowledge of where elk go locally during warm and cold weather.
During October things change. In the early part of the month elk are still rutting, but you may not want to eat an older bull--and they're "cowed up," not likely to come to a call. When the rifle season opens around the 20th some big bulls may still be with the cow herds, but as soon as they hear pickup trucks and camps being set up they tend to buddy up and go elsewhere.
On public land you may find a herd bull with cows on opening morning, but after that they're in deeper pockets on north slopes. Or they head for big ranches where there's limited or no hunting.
If you can draw a limited bull tag somewhere the odds are better for a mature bull, but even then your odds will often be better on nearby private land.