The discount is only good through Thursday 9/29 per the offer (and it's only a 10% discount on campsites):
https://disneyworld.disney.go.com/special-offers/summer-offer-room/
When I looked for rooms 9/26-9/29 I see only a discount for Premium sites ($117 ----> $105 per night). When I run those same dates looking for regular Room rates, I get availability in all but Tent.
Going day-by-day to get you from 9/29 to 10/3 there is nothing at any level, discounted or not. Likely that's due to all the 50th anniversary for MK bookings. The discount is good for dates starting July 11 (after the July 4th holiday travel binge) so there might be discounted sites available in late July, August, and early September (likely not around Labor Day). Or even rack rate availability.
Honestly, I'm not that motivated to try to fill an empty campsite for a $12 per night savings. If I wanted to travel in this period I would already have made that reservation. So IMO (and you didn't ask for it), this is an offer to say there was an offer, but we are getting scraps (if that).
You wanna camp at the Fort, my advice is book early and be willing to pay rack rate at whatever level of campsite you choose for the dates you choose.
Sorry, Shelly.
Bama Ed
PS - thanks for the find,
@G719