Considering the number of passengers affected until now, phone lines are probably jammed with customers on already-cancelled flights. I don't suppose airlines would appreciate customers calling if their flights are still scheduled. Like you say, it is doubtful, but it seems that progress is being made, what with these recent successful test flights and some airlines flying some flight e.g. KLM flew passengers to Thailand/Taiwan last night.
You could try your luck contacting the airline but changes are often only permitted if you have purchased a flexible ticket, which is typically a much more expensive fare. If you have a rock-bottom economy fare (which is what most travellers seem to go for), the chances are that changes can't be made. If they can, they won't be free - not until your flight is officially cancelled anyway.