Actually, any time I've needed to change a time or even get a FP at all for a certain ride, I was able to do it within the first 30 days after my 60 day window opened. Every time. I does take time, but I'd check several times a day, spending 15 minutes tops refreshing and eventually, something pops up. Once the 30 day window opens, I rarely try. They're pretty locked in at that point.
I rarely try refreshing in the parks. I don't like being on my phone anymore than I have to. Those pics of people riding something with their phones in their faces are just sad to me. We get what we get before we leave home. We'll get 4th and more in the parks, but usually what's only currently available.