I think dialogs should just admit their limitations. It's not annoying because it's failing to give a useful time estimate, it's annoying because it's authoritatively offering an estimate that's obvious nonsense.
So, estimate however you like, based on current rate or average rate so far, rolling averages discarding outliers, or whatever. Depends on the operation and the typical durations of events which delay it, so you might have different algorithms when you know the file copy involves a network drive. But until your estimate has been fairly consistent for a period of time equal to the lesser of 30 seconds or 10% of the estimated time, display "oh dear, there seems to be some kind of holdup" when it's massively slowed, or just ignore it if it's massively sped up.
For example, dialog messages taken at 1-second intervals when a connection briefly stalls:
remaining: 60 seconds // estimate is 60 seconds
remaining: 59 seconds // estimate is 59 seconds
remaining: delayed [was 59 seconds] // estimate is 12 hours
remaining: delayed [was 59 seconds] // estimate is infinity
remaining: delayed [was 59 seconds] // got data: estimate is 59 seconds
// six seconds later
remaining: 53 seconds // estimate is 53 seconds