Using @Vince's answer to the earlier question I am gaining some control.
My code now reads:
inputFileGDB = <file_geodatabase_where_all_work_is_done> arcpy.env.workspace = inputFileGDB fcList = <list_of_feature_classes_including_"rwc_aurukun"_as_first_member> sr = arcpy.Describe(fcList[0]).spatialReference sr.setFalseOriginAndUnits(-400.0,-400.0,10000000.0) # from Vince arcpy.CreateFeatureclass_management(inputFileGDB,"RWC","POLYGON",fcList[0],"SAME_AS_TEMPLATE","SAME_AS_TEMPLATE",sr) arcpy.Append_management(fcList,"RWC","NO_TEST")
and the properties of the RWC feature class are now:

The only glitch is that 25 self intersections still remain but these now seem tiny and after a Repair Geometry were gone.
Executing: CheckGeometry C:\Temp\DCDB\Staging.gdb\RWC C:\Temp\DCDB\Staging.gdb\RWC_cg Start Time: Fri Jun 03 12:35:37 2016 WARNING 000442: self intersections at 12986 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 16714 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 20151 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 26613 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 26629 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 29669 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 30888 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 32727 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 32867 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 33207 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 35415 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 38105 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 38197 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 39605 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 41180 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 41498 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 41501 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 43195 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 44768 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 45215 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 45644 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 46692 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 52702 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 53066 in C:\Temp\DCDB\Staging.gdb\RWC WARNING 000442: self intersections at 55112 in C:\Temp\DCDB\Staging.gdb\RWC Succeeded at Fri Jun 03 12:40:28 2016 (Elapsed Time: 4 minutes 50 seconds)
Adding one more zero in the code above to make the line below resulted in the appended feature class having no geometry errors.
sr.setFalseOriginAndUnits(-400.0,-400.0,100000000.0)