Thank you, HappyCat. Are you saying that our x86 SQL 2005 Server executes a 64-bit DTEXEC binary? If that were the case, would we not also see failures with the original package, which continues to run just fine?

Our SQL Server does not even have this path: C:\Program Files (x86)\Microsoft SQL Server\100\DTS\Binn\DTEXEC.Exe". As far as I'm aware, the "Program Files (x86)" folder only exists on x64 machines.