By fiddling with landscape generation in the scenario editor, I realized two important things:
The game only has 45° slopes and no concept of drops/cliffs
What this means is that if you want a peak at Z coordinate 80, and your base land level is at Z coordinate 1, the game will to go from 80 to 1 tile by tile, one vertical unit at a time. This means peaks take a lot of space on a map.
Higher peaks need larger maps
On smaller maps, the game seems to "hold back" on altitude, possibly because of the above requirement. 512x512 maps are never going to get big heights. 1024x1024 start getting altitudes in the 60 units. I tried a 4096x4096 map and finally got things in the 80 units.
I did not manage to reach anything near the maximum of 255 units.
Other important settings
Alpinist, not surprisingly, seems required for this to work.
Maximum Map Height
This seems to be a cut-off point rather than indicating a range. Setting it to 255 (max) does not seem to suddenly create higher mountains. It does change the altitude colors in the game though, so it seems best to keep it close to the maximum height generated based on the other settings.
If the settings give a maximum height of about 60 units, setting this to 65 means the highest altitude will show as white on the map.
Rough to Very Rough seems needed to get sharp mountains. Still, the game will often create plateaus, sometimes large ones, on top of mountains.
Keeping the Smooth setting will create spread-out hills of low altitude. Not what we're looking for here.
Medium or High seems to give good results. Lower settings seem to either create a mostly flat land, or map cut in two halves, one big mountain and a valley.
The Very High setting seems to cut down the size of mountains too much.
I didn't fiddle with this much but I assume a Very Low setting is better if you still want valleys not covered in snow (though fiddling with the Snow Line level might also do the trick).