Your crazy... lol. But I get it. We all have our dream hunts but yours is a little easier to obtain.
There are still plenty of hard to draw antelope units, even as a resident.
My parents have hot 4 sheep between them but for some reason it just doesn't interest me.
10 years ago I probably would have said sheep or goat but the reality is I am not really that interested in top of the mountain hunting like that. I think many people like to pretend to be sheep/goat hunters but in reality it's more about showing off pics than it is a true passion. It's pretty easy to tell the difference in guys who love being in sheep country to those who just want a picture with a dead sheep.
I also think that part of the choice is who could I share the hunt with and antelope hunting is very family friendly. Spending weekends cruising the red desert looking at antelope would be a lot of fun IMO.
But I certainly understand why everyone has different answers. Different strokes for different folks.
I think that another fun scenario would be having 24 hours in Yellowstone to hunt. Or even 24 hours to trespass a private ranch where I have watched animals in the past.