It is impossible to Z Scale correct areas.
area_integrate is a dangerous module for just this reason and it appears you’ve made some serious errors.  You NEVER should compute areas with Z Scales other than zero (0.0) or one (1.0).
For example.
  • The area of horizontal plane is unaffected by Z Scale
  • The area of vertical plane is directly proportional to Z Scale
  • Complex (e.g. topographic) surfaces have a complex relationship to Z Scale.
A Z Scale of Zero (0.0) provides the PLAN VIEW AREA of a surface provided that surface is not multi-valued.  If you compute the area of a plume (something three-dimensional, you will not be getting its plan view area because you’ll be getting multiple surfaces (it is multi-valued).
A Z Scale of One (1.0) is generally only appropriate for a topographic surface if you want to determine the surface area in order to know something like the amount of “sod” that would be needed to cover some rolling hills.