With such a vast number of films I would be tempted to employ a strict 5 minute cut off. If it sucks or is only average after 5 minutes move on. Every time you sit down to watch something expect it to take 5 or 6 movies before landing on something that you want to continue. Just go on a ruthless run and gun tear through these filmographies.
You won't be able to claim you've "seen" everything in the ICheckMovies sense of the word, but you'll keep your tempo up, and you'll get a taste of a lot of things in a little time (which is it's own kind of knowledge). And the things you do see in their entirety, you'll be seeing because you're enjoying them.
Imagine for instance a director whose work you haven't seen at all and they have like 15 films. Traditionally one would select a couple films to watch, hope they they are representative, and then see them through to completion. It may be that you don't end up enjoying either film and you're interest in delving further into the director's filmography is low, and so you move on to someone else (hoping, but also always wondering, if what you did see was characteristic of that director's style, and that you haven't missed something you may have loved).
OR you could watch 5 minutes of all 15 films and get some quick answers. Treat it like a wine tasting. Generally a quick sip is enough to know whether you should buy the bottle. You're looking for films that immediately fire you up. You may blow by one or two that may have developed later on, but in that way you're no worse off than the other approach which leaves some movies unwatched altogether.
I dunno, maybe it feels a little disrespectful or unfair to see 2 minutes of a Frank Capra movie and be like "f this" but whatever. If he's never made a movie you've liked yet, and you're already scraping the bottom of his barrel, do you need more than 2 minutes?
Generally speaking, good movies don't start by being bad movies, so you can't go too wrong imo.