I've been on reserve much of the last 3 years ... have had "reasonable" success moving/dropping R days. Like someone else said, when I've been unsuccessful and had a really good reason why I needed certain days off, I've had good luck calling/emailing My ACP who was inclined to take care of moving them for me ...
I've also had some luck calling the scheduler and explaining that the "disapproved" just didn't pass the common sense test. (i.e. trying to swap to a day when there were fewer folks on reserve and more open time?)
It would be hard to call in sick after your move/drop request was disapproved.
Good luck
Mark