I have a reservation at Saratoga Springs for the month June and there is very limited park availability. I won't go if that is the case, but I thought it was interesting that even staying on property we can't get into all of the parks. Does anyone know if Disney releases more availability as time goes on, right now there is only Epcot and some days there is the Animal Kingdom.
Those staying on property, those having Annual passes, and those staying off property with normal tickets take out of different availability buckets. While the website *should* check all those buckets and take from any that have availability for which you qualify, the website sometimes fails and people have had to call to get their reservations.
Looking at the 'off property normal ticket' calendar, I see good availability for MK from June 19th on. So if you're not seeing that when you are logged in to your 'on property'-linked MDE account, you can try calling them. Or unlinking your Saratoga Springs reservation, making the park reservations, and relinking SSR.
That said, Disney (thus far) has not been adding availability.