You should keep checking SOG for openings. That's how it's worked for me before. Even this trip coming up in fact, we changed our itinerary and were going to be early. But, the SOG was sold out the days I needed, I kept checking and there ended up being an opening. I was able to change our reservation to the timeframe we needed.
Other suggestion is to see what Disney resort you'd like to stay at, and call the reservations number and ask if there is availability at that resort for the days you want, with military discount. Check the difference between that rate and any other discount rate that may be applied.