I respectfuly disagree to some extent, though your expertise is obvious.

We do have, or had a class of tactical nukes, very small, low rad yield. Most delivered through cruise missile, some were actualy cannon fired.
Was this class of weapons removed from the arsenal?

And the use of n-weapons would instantly turn the majority of the world against us. We will have to have the cooperation of most nations, gladly or grudgingly, to deal with the extremely difficult military actions to come.

Our conventional forces are sufficient to deal with the task at hand.
The introduction of the nuclear card to the table would destablize the whole coalition.