I have had award tickets changed at the airport (usually not at the counter, usually at the gate and almost always club agents will do it.) I have been put on earlier flights, had coach award tickets upgraded to F and even been put on direct flights removing a stop.

I've also been told "NO" either because it's against the rules (which it is) or because while the seatmap looks open, the flight is in reality sold pretty tight.

So go prepared for rejection and hand an A&B if they give you what you want (or better - an F upgrade.)

NOW, the reverse scenario is more problematic. If you "miss" your flight your reservation is canceled - you would have to call and hope you could change your ticket to a saver seat on the later flight or pay more miles for a seat on the later flight. Except for the "flat tire" rule, I don't know of any way to fly later than originally booked without great difficulty. You could try going to the airport to do it first thing in the morning on your day of flight and hope they can change your ticket.

I think a lot of it depends on when you're flying too - a weekend in the summer - fuhgeddaboutit - but off peak destinations, hours and days you might have a better chance.