I got the task to run (I can't figure out why it is behaving itself now though).
Task Scheduler still reports error 0x41301
, but the Process Explorer window appears and it is in Administrator mode.
The weird thing is that I have to enter a password when I try to create the task for my user account, but if I change the user to "Administrators" group, I don't have to enter any password!
Surely a user shouldn't be able to create a task for an Administrator (without entering a password)?