Seriously??? While I agree that the answer shouldn't change on this, and understand the answer given was likely the truth and the procedure, c'mon...is there any answer that might not change if you hang up and call back again? Really??? This is DL. The company motto is "If you don't like our answer, hang up, call back and we'll probably give you a different one."

You can call and ask if the agent is speaking on the telephone with you, hang up, call back, ask the same question and get a different answer. Inconsistency is a way of life at DL. The fact the second agent is talking to you on the phone doesn't matter. The agent will have to tell you "no" because inconsistency is the rule. You can either get frustrated by this fact or use it to your advantage.

At the risk of sounding like Gloria Loring (Robin Thicke's mother), there you have the facts of life.

BTW, on the OP's question...a strategy that sometimes works in overcoming the non-availability issue when changing awards tickets is to move your ticket to a different set of flights entirely, and then move the ticket back, but it's best done as a SDC, so you would have to wait to the day of travel and take your chances.