In actuality, you are not supposed to be granted
TN until you are actually entering to work. As you point out, there is leeway available to the officer, but the Western Division does not give such leeway (as is their right). TN is an entry status, thus you are granted it when entering to work on that status. It sucks, but that is how it is.
You don't need it in advance to work, so why try to piss them off by asking their super to override them. That is a guarantee to be denied as they will fine-comb your petition for every misspelling and typo.
The correct approach was to have the TN letter NOT specify your start date, and to arrange working teleconference with your employers (at a coffee shop across the border). Then you could have truthfully answered "yes" when questioned if you are going to start work now.