Rate seems to differ from the rate I’ve booked. Can I get applied the newer ( and cheaper ) rate?

We (=Property) are always fully able to change the rate by our own decision.
If you (=guests) want to get applied the newer ( sometimes cheaper ) rate, you have to,

1. Cancel the existing booking for your own self.
2. Make a new booking for your own self.

In this case, note that,
1.You have to pay 100 percent cancel fee ( We never discount/waive the cancel fee for any reasons) for your existing booking.
2.You have to pay for the full amount of your new booking. Cancel fee for the existing booking will never reduce the payment for your new booking.
3.Your room might be taken(booked) by some other guests (We never guarantee the availability).