Mike,
This isn't the thread I'm searching for for you, but this has some 18" info;
https://www.renntech.org/topic/17095-need-18-tires-how-big-can-i-go/
Here's a more informative thread;
https://www.6speedonline.com/forums/cayenne-955-957/252459-anyone-running-265-65-r18-3.html
If you'd still like more 18" options, LMK, and I'll look up the most informative thread (it's on my work computer).
I think what HUMMER meant was Can YOU repair a Cayenne in the middle of Mongolia, with tools/parts you brought with you? Yes, the Transsyberia raced across Mongolia, but IIRC they had full support crews from Porsche Motorsport technicians to help with any field repairs. If you're a Porsche technician, you could repair if you brought enough tools/parts. But for the layperson, can you easily access components? Do you have a computer scan tool with you to read fault codes, perform actuations, diagnose an issue with the vehicle and then have the parts/tools to repair? Most modern vehicles have the vehicle manufacturer engineers stuffing a whole lot of "10lbs of ******** in a 5lb bag"(ie engine bay).
A LandCruiser might be more reliable (they're simpler than a German engineered Cayenne), but even if a LandCruiser broke in the middle of nowhere (let's say an axle broke somehow), unless you have a spare axle and the tools to repair, you won't be repairing it in the field. So...to that point HUMMER, no vehicle is an infallible long distance/remote travel vehicle, unless you're carrying every possible spare part with you. Could you use your SatPhone to call in the spare part/tools and repair in the field? Possibly. But to that point, if driving a Cayenne anywhere in the world, you could use your SatPhone to call in a Master Porsche technician/parts/tools and repair in the field.
Now, if your SatPhone can't communicate to someone, then it could be a long walk to an area where the SatPhone works. That's an adventure.