It's now enabled that he will take office, but he's still gotta go to the courthouse and be sworn in to accept his new position.
If he doesn't, or there is any possibility that he can't or won't, then Irresistible Grace and Perseverance of the Saints is false.
The problem remains and is compounded with the free will choice and robot objections.
So yeah - your objection noted, we stand on the Irresistible Grace principle.
Probably the toughest thing for us to explain is that 'free will' bit. I don't have a good answer for that except to say that I feel like I could have rejected Christ, but also had felt drawn, and am pleased (of course) to have accepted.
Clearly, we believe there are times and places in which people are steered directly by God (the scripture writers, for instance, were 'God Inspired'). Pharoah's heart was hardened in Exod. 7:13. But I see no scripture declaring that God orchestrates and directs the minds and actions of all men. To the contrary, if man is being controlled, then how could we all possibly be "without excuse" before Him (Rom. 1:20)? We would be able to say we were controlled! So either that verse is false, or we do indeed have free will.
Hmmmm - guess He gave me those words to write... or did He?