Is there a button available to users that will cause stories posted by pages and friends to actually show up in the news feed? It seems like there is no solution available on the receiving end.
If you make a friends group that includes all your friends it will post everything in chronological order with no in feed ads or crap from pages you've liked. It's far superior to the news feed IMO.
Not the simplest UI but: goto the friend's timeline. There should be a Friend button with a tick next to it. Hover over the button. On the pop-up menu the "Show in News Feed" option is probably already ticked. Once it is, choose Settings and then choose "All Updates" or whatever as appropriate.
AFAICT there is no solution on the receiving end. Your feed is going to be filtered or delayed by the Facebook gremlins and there's nothing you can do about it.
The internal heuristics generally seem to get it right eventually: I see true friend and family posts with essentially random delays of sometimes up to 2-3 days, but I don't actually miss any (I don't think).
I don't even bother trying to follow stuff I'm interested in on Facebook anymore. G+ does that sort of thing better anyway, at least for all of my interests.