I'm thinking somewhere around 9,000-10,000 would be the highest you could drive in North America and still have a road/trail to follow.
FWIW, Last year, I piloted a Samurai with the stock, Hitachi carbureted 1300cc engine over Black Bear Pass. Black Bear Pass is 12,840 feet, and many of the mountain trail passes in Colorado have similar elevations. Once I was above 11,000 feet I had to perform the gas, clutch, and handbrake shuffle. That really made it interesting on the first section down, aka The Steps.
The key was to keep my foot on the gas, but the 5:1 gears and 29" tires enabled me to crawl at a snail's pace. I'm sure that the engine output was likely less than 20hp at that elevation, but the engine kept chugging along.
Once I descended back to around 11,000 ft, the engine idled fine.
Next week I plan to pilot a Samurai with the 16-valve 1600 FI engine up Pike's Peak. I'm sure that there will be a huge power loss at 14,000 feet, but it should idle as the FI will be able to compensate for the thin air better than a carburetor with a feedback loop. I will report back my experience.