So switchbacks are usually shaped something like this:
and given that they were originally dwarf-built I sort of expect them to be something like that.
So making them more secure involves cutting some additional road space out of the inner edge of the curve, and probably moving dirt from the upper road onto the lower road, such that they're brought to become more level, but made more steep in the process.
The other option is backing the steam wagons down, then getting a crane capable of lifting them up, then down onto the lower road. But that sounds crazy with something the size of a monitor.
If we end up needing to stop for a few weeks to let work crews fix a curve in the switchbacks it's possible that we'd be able to free slaves from either Uzkulak or the Steppe tribes to use as labor in that.