Gator29,
I don't know about specific loops being open but wanted to make a comment about grass and suggestions where to request.
Since you've been there and had the swamp, you know that there is a lot of tree cover over the cabins. They are also fairly close together IMO so there is not a lot of grassy spots or space for such.
This is a typical cabin from Google with about as much grass as I've ever seen at a cabin:
It is more common to have lots of pine straw and maybe a few brambles and palmetto bushes around with little grass. Something like this:
What I would suggest to you is the far ends of 2200, 2400, and 2600 (the right hand ends of the loops on this map):
The outside of these loops back up against the big grassy/open field that would be an easy walk from your cabin porch to a grassy open place where you could play with the dog or throw the ball. Cabin 2222 in this article is an example:
https://wildernessprincess.net/2020/09/05/the-8-best-cabins-in-fort-wilderness-and-how-to-get-them/
See the big open grassy field in the back of this picture?
That's out by the hitch/un-hitch area and it's easily accessible from the cabin porch.
So my advice would be to get to the Fort as early as you can on your check-in day, walk into the lobby (or in your pull-thru check-in lane) and negotiate an outside cabin site in one of those 3 loops that backs up to the field. Disney will pre-assign a cabin site to you but they will try to swap you to an available one if it is available and if you ask. That's kind of a hard request to make in a few words in a reservation note in advance.
But if you're polite, patient, and flexible, the CM will try to meet your request.
Just my two cents.
Bama Ed