There may not be any preferred rooms available for those dates but I don't see how they can book up all the AB rooms since they area spread across the various categories - as someone who ended up with a Mansion and AB room last trip.
I would go ahead and book a POR room and keep checking for availability for a preferred room (to guarantee AB). You're closing in on the full trip due date and I feel like a lot of rooms open up at the 60 day mark.
I also like your dates! We were there 6/24-7/1 last trip and the crowds weren't terrible... early mornings and late nights had us walking on most rides for the first hour and 5-10 min waits during PM EMH at MK. Plus, when we lived in Florida I felt like each day of summer grew more humid than the one before it... hence why we're doing Sept instead of August this year!
My info is from before the new
MDE was introduced, but I was able to pull up the newest resort info in my Disney account and view the details (room/price per night) with the rezzie #. Any changes are supposed to automatically generate an email but I found I only got 1/3 of the emails. You can call and have them resend it (I would just wait until Sunday or Monday since the new offer just dropped).
TA is helping me get everything lined up to try to grab FD when offer is released to public next week. I did a prelim authorization so she doesn't need to check in and can just jump on it... *fingers crossed* It would just be the most amazing thing if we can swing it for all 4 rooms -- no sharing, and even military/AP discount wouldn't cover 4 rooms! The only downside is I won't get my AP (since you have to get tickets with the offer) but it's worth it to potentially save the fam $$$.
***Funny/sad story: my parents are traveling and hit up a mall that has a Disney Outlet. They called and asked if I needed anything and relayed that I hadn't been lying about the Frozen mania. Apparently a CM brought a box of merchandise out (swim stuff) and people went NUTS! It even said "summer swim essentials" in marker on the side!
Even better, my mom was looking for cover ups for DD6 and asked me what the snowman's name from Frozen was (I guess 'In Summer' was playing on the TVs). I told her and she said "Olaf, that's right" and a bunch of people came over and said "where? Where did you see Olaf?" She stood there for a minute and explained she was just talking. The CM shook her head and said "Oh, you can't drop names like that in here... people go nuts." My mom couldn't believe it.