Ping Pong is interesting but ultimately doesn't stray that far from a standard sports story apart from the animation style. I think it's one of Yuasa's weakest works, and I would recommmend the likes of Kemonozume, Kaiba, and The Tatami Galaxy a thousand times over it.
Not an animu/mango but the visual novel Forest is the most insanely confusingly brilliant thing ever.
Have you seen Jin-Roh: The Wolf Brigade, Blame!, Texhnolyze?
tatami galaxy had a lot of fast speaking and an art style that was really unusual but worked excellently in that specific scenario.
The melancholy of Haruhi Suzumiya episode 28 was unusual as it had a load of scenes that were like 5 minutes long of a room, yuki silently reading, and dialogue from the drama club next door. It's probably the most comfy episode of anime I've seen. The entire series also takes a dump on chronological order and has the endless 8.
I suppose I'll plug bakemonogatari simply because it's new wave cinematography.
They're all pretty popular though so I imagine you've probably already seen them.
Pretty much everything by Taiyo Matsumoto works (the guy who made Ping Pong), the art style by itself is pretty unique, at least in the manga industry. Try with Tekkon Kinkreet (which also has a movie) and Takemitzu Samurai, those are great, and also go with Sunny, I'm reading it and it's beautiful.
And in anime, well, I think we all agree that Masaaki yuasa's work is a must watch. Also, check out Tenshi no Tamago by Mamoru Oshii, I barely know what it is about, but I don't care either, besides the fact that it makes no sense (or I'm the one who is a little dumb, I don't know), it's great. Something by Katsuhiro Otomo might be good too, he has some good anthology films, Robot Carnival, Neo Tokyo, and Memories (which I haven't seen yet, but is a classic).
All of these are really good recs. I'd add on Kaiba and Kuuchuu Buranko, I just finished up both and they're the most alternative/"breakaway" styles I've ever seen.
I'd recommend anything by the late Satoshi Kon, whose works are almost always off-beat, psychological and weird. Some of his more popular stuff includes Paprika, Millennium Actress and Perfect Blue, and perhaps Tokyo Godfathers, if you're looking for a spiritual experience.
It's a pretty literal interpretation of what you said, but Angel's Egg has almost no dialogue while still managing to be deeply expressive. Mind Game is quite unique, as well, since it switches constantly between different art styles. If you want something really wacky, try that. Cat Soup is another great example of a story being told without dialogue, mostly through a series of metaphors and dream sequences. I've not seen all of them, but Shigeru Tamura's work probably fits into the same category as Cat Soup: Glassy Ocean, Minor Blue and A Piece of Phantasmagoria. From your Lain picture, I'm guessing you've already seen that, but make sure to check out other stuff Yoshitoshi ABe's worked on. Technolyze was already mentioned, and Haibane Renmei's got a lovely feeling to it. I've not seen any of his other stuff, but I trust my main man Y to the A B enough to know they're probably good. There's also stuff like the End of Evangelion and FLCL, but everyone and their grandmother's seen that, so it's probably not worth mentioning.
That's all I can think of off the top of my head. Will post more if i can think of any.
Maybe this isn't what you're looking for, but there's always Cat Soup if you haven't already seen it. MindGame is another one that I almost never see mentioned, despite it being one of the most unique animated movies I've ever seen.
cat soup is that trippy one with the brother kitties right? I'd say that pretty much fits OP's request.
I was going to suggest Mind Game but OP asked specifically for very experimental stuff like stuff without dialogues and the like. In that sense most of what has been suggested are pretty much regular stuff.
I guess this is a really old anime but it was one of my favorites. It's really comfy and some of the hand animated scenes blow me away. Has rotoscoping and I know that's a popular technique but it's done very well in this anime. Bobby ni Kubittake Sorry if this isn't what you're looking for.
i'd highly recommend genius party; happy machine is one of my favorite things on this planethttps://bakabt.me/torrent/146806/genius-party-bss