However, I would like to cut these extruded buildings and have them terminate at either the top or bottom face of the "base". Is there some was I can either delete the object past the face or split the mesh at a face to make it easy to delete all the extra material underneath the base? Thanks!
I think you can easily join all buildings together into one object with Alt+J, then use Bisect that is next to knife and cut it along the plane very easily... After that select your city, go to edit, press A to select all vertices, right click it and select Separate by Loose parts... All your buildings will be cut and as individual objects
You can do this or either use boolean to use plane as cutter to divide objects into two and delete bottom part