RE: What would you do in this situation?
What unit is it in? If all the elk tags for all seasons are limited, which it sounds like they are, the landowner can apply for up to 6 vouchers that he can give to anyone. They can use them for a tag for any season and can be used on private land or public. Therefore, if the landowner was willing to do it, you might be able to hunt with a muzzleloader next fall. He/she would need to " register" the land the first part of January. This is a new program, only a couple of years old, so he may not know about it. It is talked about on page 3 of the big game brochure.
If that is not an option, then I guess it depends on what elevation the ranch is at. If it is mainly high country, I would wait for the muzzleloader season. If it is lower country, and snow will drive the elk down onto the property, then go to the 4th season.