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I also noticed that, in the pcd, streets that are supposed to be flat, look slightly bent in the z axis

I believe this is the root cause that you can't give correct z coordinate. This "bent" cannot be avoided if you are using ndt_mapping to create large maps. If you want to use gps with large environment, then best solution is to ask some companies to create accurate HD(pcd) maps for you. (like HERE, Carmera, etc.)

I was thinking to project the GPS point (i.e., the derived UTM coordinate) into the pcd to get the corresponding z value.

This could work, but it's also very likely that your x,y coordinates are wrong in some parts of your map if the map is "bent". I think it is more appropriate to find a way to get accurate pointcloud.

FYI, PCL library functions in ndt_matching uses float to express x,y,z values. If you are having very large UTM coordinate values, then that may be worsening your ndt_matching accuracy.