I find that if the surface is in the XY plane, the elements are numbered in your preferred order. Look for the ID number on the bottom edge of the image.
When the surface is in the YZ plane, the element IDs are numbered in an odd way that you showed.
Why do you need the elements ordered in a particular way?
Users sometimes need to map results from one analysis to be the load on a new analysis. For example a Steady State Thermal analysis calculates the temperature distribution on a surface. Those temperatures are to be input into a Static Structural analysis to calculate thermal expansion in the structure. The way Ansys imports result data from an external program to use as a load is by XYZ coordinates. In that way, the element numbers used in either analysis are irrelevant and the mesh can even be different.