Don't quote me on this, but I have a friend who works for a Disney travel company, and he says that WDW releases some more FP's at the 30 day mark so non-resort staying guests have at least a fighting chance to get FP's. It doesn't take too much time to check on FP's, I would just pop onto the app a couple times a day and see if you get lucky. Given what my friend has told me, I would get on first thing in the AM on the 30th day prior to your stay and see what happens.