We had schedule changes on our award tickets last weekend. I called in, because the website told me I HAD to, to make changes. Before calling I looked at all the available trip options for the same dates of travel (dates could not be changed). I found flights that I "wanted", and in the past have had no trouble getting them to make the change.
However, the representative made it seem that she was going above and beyond her duty by giving me the flights I now wanted. We originally booked a departure flight at noon, but now wanted a 7:30am flight. She gave me some story about, "okay, we'll do this, but just this one time....blah blah blah".
Also, I called the number on the back of my SM card, but the first lady said she couldn't make any changes because it was an award ticket and transferred me to the "SkyMiles desk"
Needless to say OP, YMMV.