How do you calculate the CPU Affinity Bitmap?
Your binary representation of the mask should be:

1100 0000  0000 0000  0000 0000  0000 0000


Converting that to an unsigned 32-bit integer would equate to your original calculation:  3221225472.

But the affinity mask tasked a signed 32-bit value.  In that case, the binary to signed 32-bit value would be:  -1073741824.

Same bits, just different interpretation/conversion (signed vs. unsigned).


  I can't use the GUI, because all my processes need to be reusable on Server Core instances.


As an aside, you can and should use SSMS remotely, so the fact that you could have target database servers on a server core OS shouldn't prevent you from remotely using a GUI (like SSMS).  On that same note, I always prefer T-SQL at the very least for reusability and for documentation purposes, if nothing more than just knowing exactly what is happening when you do something with no GUI tricks/abstractions/assumptions.