I am running ArcGIS 10.3.1.4959.
I downloaded gdal18.dll from GitHub. Both my installed copy and the GitHub copy say version 1.8.0.10300, but my installed copy is 7.87 MB and the GitHub copy is 9.48 MB. Although the names and file versions are the same, obviously the files aren't the same. I will move the GitHub copy over to \bin and test it shortly.
Regarding the Whitehorse GeoPackage, what table, data element, etc... are you using to determine an invalid spatial reference. The gpkg_spatial_ref_sys table does list undefined Cartesian and Geographic coordinate reference systems, but it also lists WGS84 and Web Mercator. The gpkg_contents and gpkg_tile_matrix_set tables state Web Mercator as the SRS ID.
UPDATE: Tried the GitHub gdal18.dll, same error: 000582. Something else I noticed, 150+ ~10KB SQLite files were created in my %TEMP% folder. Does this seem right? Are they supposed to be cleaned up at some time or will my %TEMP% folder be filled with these files?