So basically, the way it works is when a deal drops, you can go into your
MDE and see if you can apply the deal to your room. This isn't really applying the discount to your room, but seeing if a room in the same category you already booked is available under a discounted rate. Disney essentially sets aside specific rooms for the discount, so you cancelling your non-discounted rate would be unlikely to send that room to the discount rate pool. Here's a few examples of how this could work out.
1. You go into MDE, click the change offer option on your reservation and it says a lower rate is available, and you're able to change it then and there. Yay! You're all set with the discount.
2. You go into MDE, click change offer option and it says no availability. This only means it's not available for all dates. This is where you might need to do some sleuthing on your own and play around with dates to see what comes up. So, for example, if your dates are 12/5 - 12/12, you might start searching around and find that you can get a discounted rate 12/5-12/9 in a standard room, but 12/9-12/12 in a water view room, or maybe not at all. In this case, you can change your dates on your reservation to match what's available, then make another booking for the remainder of the dates (make sure you search for those remaining dates to make sure something is available!). You will end up with separate reservation numbers and if there's a difference in room category, I would expect to have to move rooms. If there's no difference in room category (if say first half of your dates came up as available on the discount and the other half did not), Disney will do their best to keep you in the same room.