How many people in your party? We are a group of two and it is so easy to pick up same day, even for rides like 7DMT and FoP. I even got Slinky 2x in one day and I wasn't glued to my phone. I would think it's much easier the fewer the people, but you can often split into smaller groups and find overlapping times (remember you can tap in 5 minutes before or 15 minutes late and it's built into the touchpoints).
I just refresh and refresh while in line, waiting for food, etc. Usually it takes a few minutes of refreshing but there's always a lot of waiting time to use. I probably spend 5-10 minutes at a time refreshing for headliners, and 1-3 minutes to find more middle of the road stuff like BTMR, Everest, Safari, etc. I'll give up if I don't find anything and try again later but I almost always do. When I say refresh, I mean reloading the FPs very frequently as in you're tapping and tapping constantly during that time.
We also stack our first three FPs and try to have them done by lunch time because the best odds for picking up FPs are usually before dinner time. The pickings get slimmer in the evening but it's still always feasible. If it says FPs are done distributing you just hit back or whatever and try again. Sometimes I get bored and do this even when I'm not in the park since I have an AP (gotta maintain those refreshing skills

) and even during the busy holiday season it's possible. Maybe less headliners but certainly additional FPs throughout the day.