I think if you want to take advantage of the Saver rate, one way or the other they are going to charge you to redeposit the miles. That's just my reading of the reg's, but if my interpretation is correct:
1) You can cancel the Standard Award ticket, and book the Saver one. You ask for the miles to be redeposited and pay the fee for that.
2) You can change the ticket (if they allow you), eat the close-in change fee, and then they hit you with the redeposit fee for the price difference.
If that's true, then what I would do is just change the ticket to some other future travel plans and book the Saver for this trip (assuming you have the miles).
All of that said, it really comes down to how much time, hassle, and money (fees) it's worth it to you to save on this ticket. It can be done, but it will take some amount of all three, and you just have to decide how much trouble it's worth for you.