I'm working on a concept for a terraformed world with artificial mountain ranges/plateaus that stretch higher than a natural formation possibly can. I picture them like extremely tall table-top mountains where people and animals can live comfortably on top. The water content of the planet is similar to Earth's but perhaps with much shallower seas. The planet will also have a much thicker atmosphere, though how much thicker may depend on how high a mountain can get.
Here's the rub: the mountaintops and the surface should be at extremely different atmospheric pressures. For the effect I'm interested in, where traveling on the surface is an extremely taxing endeavor, the mountains will need to be 30-50 km tall. As far as I know, because of gravity and the strength of different types of stone, Earth's mountains can only be about 15 km at their tallest (Everest is about 8 km).
The terraforming of the world will be performed by giant machines, possibly everything from bulldozers to giant extruders that pull up mantle material and print it onto the surface of the tectonic plates. So fewer glaciers and erosion, more giant machines.
I've only come up with two possible ways that my artificial mountains could achieve such towering heights with the same planetary gravity: A specifically designed type of stone that doesn't occur naturally (and therefore has the strength to hold together inside such a tall mountain). Or, to somehow surround a metallic core (such as the giant machines needed to build mountains) with more typical types of stone.
Assuming that power and materials are effectively unlimited, how could these mountains be created?
If you have any other suggestions, I'd love to hear them too.