I just called for AP rates for our stay June 11th through the 14th. Here is what was available:
Port Orleans FQ for $223.88 (per night includes tax) but that room was with 1 King bed and there are 3 of us, so it won't work.
The other availability for that time (and not even necessarily) was for Animal Kingdom and Grand Floridian, but both of those rooms would have been suites so I didn't even ask about pricing!
The good news is that I was able to extend our Pop Century reservation by one night, probably due to others switching UP to new resorts so THANK YOU! When I called earlier this week, June 11th wasn't available at Pop Century (and we were already booked for the 12th and 13th) and today they had it so now we don't have to stay off-site for that first night. Even though it costs a little more than the off-site hotel I booked, it's worth it to be checked-in on-site for all 3 nights!