Move generated Triangles up or down a specific amount


I am using a script I found here in the forums to create a random assortment of triangles within a boundary. It creates 2d Triangles, based on points of the boundary and a slider to control how many triangles you want. I am wondering if there is a way to modify this script so I can move the vertices of the generated triangles up or down a specific amount, also at random. I am trying to create surfaces like this (see the highlighted surfaces)

Which look like this in section (sorry for the bad image)

I have attached the script, again, not my creation, taken from this forum. (7.7 KB)

Basically I want to say, ok move vertices either 6" or 1’ up or down to create these faceted/articulated surfaces. Right now I have just been moving the vertices by hand after baking the results from the above script (which yields closed curves which I make into surfaces).

Thanks in advance! (15.1 KB)

Thank you! This is awesome, works perfectly.