The "working with" stuff did get a number of conservatives bent out of shape (such as Evans & Novak I recall), but they didn't know how deep the Reagan plan to undermine the Soviets had progressed...and that working "with" the Soviets (but only after the defenses were rebolstered and SDI on track, and the "freedom campaign" underway) was part of the design! There was no personal ill-will against Gorbachev (or anyone who the system, in desperation would have thrown up) ...but Reagan understood that the Soviets "peace offensive" if actually followed up with anything other than words meant that their totalitarian distopia was finished...
He adroitly called their bluff on the peace offensive. The INF Treaty resulted from his forthrightly pushing for deployments...gaining the supposedly impossible-to-achieve, "Zero Option". And then there was the little matter of the Berlin Wall:
