I have just rebooked the same award ticket for a lower price, using the "spare miles option" to secure the lower rate. (Originally 2 pax in J 226k SFO-PRG, lower price is 173k (exact same flights), now current offering is 211k after cancelling original booking). Miles were credited back fast enough (checked only after 15 minutes). If you do not have enough miles (i.e. would be changing the ticket) - then I'd do it over phone.

I know in case of IRROPS in the past (similar case as irishguy28 above) - KLM cancelled in winter schedule, rebooked on AF same day where the same price in miles was NOT available on website - FB rebooked us just fine, so maybe agents have some more options to deal with it than on the website? I would consider this a gamble though.