That's the days I was trying to get but when I looked again they were gone.
Are you looking only on Disney's website, or have you tried other travel agents? There is a travel agent who books blocks of rooms in advance through Disney's Group Reservations center. It's Magicalvacationstravel.com. Because they book blocks of rooms in advance, which they later sell to their clients, they have a different inventory pool with availability that another agent (including Disney's website) may not otherwise have.
I am actually going close to the same time frame you are wanting (May 25-31, to go for the Pandora opening). A few weeks ago they were able to book me a great deal at the Contemporary (Garden Wing) for around $300/night average. Looking on Disney's website today, the Garden Wing shows $498/night for the same dates. I found out about this company from
@lentesta by reading one of his blogs on touringplans.com and scored an awesome deal. Thanks to Len for writing about them! So they may not only get you the dates you want, but get them for you at a greatly reduced rate.
So check out their site and submit a quote using offer code LMAY17 (for the time frame you are wanting). Not sure whether or not they'll have POP available but they may have another value or moderate in the ball park of what you are wanting to pay.
Another idea to get there for when you really prefer to go, is to perhaps look into changing resorts at some point during the trip. In case the resort you want is full the entire length of stay, that same resort you are looking at may have availability some of the days, and another resort may have availability the remainder of your stay.
As far as traveling solo is concerned, I'd definitely recommend it. Do it at least once in your life. I typically travel with my family when I go, however this past November I went solo for the first time and it was certainly the most peaceful and relaxing WDW trip I've ever made. Not saying it was the most enjoyable trip, but it was definitely awesome.
Obvious reasons for a solo trip are being able to decide on your own when and where you want to go without someone else not agreeing with you. I got to do what I wanted to do. I did the Keys to the Kingdom tour and Undiscovered Future World, which most folks in my family would probably not want to pay for the cost of, except for my dad. Definitely book some of these tours if it's within your budget.
Booking FP+ for D & E ticket attractions, making last minute changes, and booking your 4th, 5th, etc. additional FP+ at MK is easier because there is more FP+ availability for one person versus multiple people. If you want to eat good food but not sit at a table alone, of course you have a fair amount of restaurants with bars (except for MK) where you can sit at and order food off the menu.
There will always be people to talk to in lines, so you won't feel too alone. On the tours, the Cast Members do a great job of interacting with everyone on the tour as well.
Sorry for the long post, but I say go for it and good luck at getting something at the end of May. Pandora is opening! then!! Woo hoo!