I'll be honest, I don't think a Catholic, especially a Tammany Boss could become President. The prejudice against Catholics was immense at the turn of the 20th century (look at Smith just around a quarter century later) and Tammany Hall across the nation was the brand of corruption. A corrupt Pennsylvanian boss would have an easier time skipping by. Tammany Hall was so ingrained for its corruption and (seen bad at that time) pro minorities and immigrants, especially Irish Catholics. Germans, even Catholic, were more accepted. So I'd have to call ASB on that.
Still really like the TL, but I don't see how this specific aspect would happen at all.
But I'm glad someone used him in a TL. He's not as famous as I thought he'd be. Tammany's Reformer.
The miner incident and the governing structure was accurate. Honestly, if you wanted (and I don't want to dictate your TL
@Redcoat), you could just replace Murphy with a Protestant New York politician who was not an enemy of Tammany (Murphy would have backed him and he would have won New York).