Heather, excellent post. You are right that he was on the wagon for the months prior to his death.

He had already had a minor heart attack in the early 1970s. His drinking, womanizing, peripatetic lifestyle, smoking, insomnia, relentless drive for new experiences, serious bout of hepatitis in the late 1960s, and aversion to doctors probably helped do him in more than Network. Finch went through periods when he was off the bottle and supposedly before his death, he wasn't drinking

He was on the Tonight Show the day before he died.

That performance didn't help his health, no doubt about that. He gave everything he had, to the point of exhaustion.
But what a way to go out!