Interesting.
How long are you going to hunt and how many people are we talking about? You might need to be gone for a few weeks at a minimum to make this work out and though they are all open the last two weeks of October it might be better to hunt the lopes and elk earlier, but the deer later when they are rutting? So optimally that is 1 month. Sounds a bit crazy, but could be an epic adventure if you have the time to pull it off!
Based on last years odds, 10% regular and 50% special for 32-Elk, maybe you all should put in individually for elk and see who draws and then the others could try for lope or deer if desired and you would end up with a few different hunts in the area and not be as overwhelmed on one hunt. This is the last year you will be able to do elk early, so you might want to take advantage of that, next year all 3 are at the same time.