No you won't have to move as long as your reservations are consecutive and at the same level.
If you end up with multiple reservations, when you check in the FIRST time, tell the CM also about the 2nd reservation and they will add a note not to bump you or reassign. And then if it were me, sometime the night before the first reservation ended, I'd wander back up to the lobby and confirm that you are in the site, are staying on a second reservation, and not moving. Never heard of anyone having to move if same level.
One time I checked in, got assigned a loop, and someone was set up on it! I called the front office and got a different site assigned (which was empty). Disney didn't make the other folks move.
If you can string together $30 a night savings for a number of your nights, it does add up. So if it works, queen, go for it.
Bama Ed
PS - when you have multiple reservations, they can NOT be merged together if one has the discount and the other doesn't. (Usually i merge them if the two are identical). So the night before a reservation ends, make sure the office has your next reservation pre-assigned to your current site number and add the "do not bump" note. Because I've bumped plenty of pre-assigned folks (nearly every time) on arrival morning. But if you are already on it, you have "squatter's rights", so to speak. And if you mention it all on the initial check-in, you probably don't even have to do the night before thing. But I have just for peace of mind.