I don't think it will change his faffing but at least now he will concede that if I wasn't around, he would probably be late for everything
Argh! That's what they want! What has basically been "proved" is that you now have to be in charge of everything for ever and ever. He will grudgingly admit that, yes, you were right and he was wrong and make a bit of a show of grumping, but INSIDE he is experiencing a huge wave of relief and relaxation. YOU will do the planning, YOU are in charge, if he's ever late for something else or makes a mistake, it won't be his fault, it will be because YOU failed to remind/supervise him.
You blinked first in the standoff.
I know I sound brutal, but this stuff drives me mad. My father had a zero-tolerance policy for that sort of nonsense and I guess it's rubbed off. He genuinely did once drive the car away without the rest of the family because he had said what time we were leaving and we weren't ready. So he left.
He has been known to tell you as you walk into a pub "Now, in a minute, the bartender is going to ask you what you'd like to drink. So if you're not sure, have a think NOW about it, rather than holding everyone up at the bar".