It’s been a while since I’ve been able to keep up with anime selections. As an example, I’ve only seen a couple of your top rated series you listed. Having said that, here are a couple older series I like to recommend.
Patlabor - A series that I’ve heard best described as being Hill Street Blues with giant robots. It focuses on a police squad in a (then) future Tokyo where construction robots had been instrumental for a major land reclamation project in Tokyo Bay. Generally excellent SF, with decent characterization. There are two versions: an OAV series with about seven episodes; and a 48 episode TV series, followed by another OAV series - then with two movies set in the TV continuity. Expect goofiness, but some good story plots, as well.
Neon Genesis Evangelion starts off seeming to be another standard giant robot TV series, then takes a left turn into surreal and floors the accelerator. It does build slowly from that beginning. For me, it was episode six when it became impossible to deny that what I’d thought was going on was very much in error. A wild ride, and the ending is a bit bizarre. Still something I recommend.
Nadia Secret of Blue Water is a send up of Jules Verne, taking and filling in around the basic inspiration of 20,000 Leagues Under the Sea. (If you saw the Disney animated movie, Atlantis: The Lost Empire, you’ll recognize several inspirations for the Disney film from this series.)
For just plain entertaining silliness, I can’t recommend the Magic User’s Club OAV series highly enough. There are some spots where I find the humor a bit uncomfortable, but generally a very touching, and positive shojo story. Oddly enough, about an alien invasion. Not dark and quirky, but def. quirky.
I’ll second the recommendation that infinitii made for Irresponsible Captain Tylor, something of a send up of a popular live-action TV show in Japan at the time, and standard space opera. You’ll spend the whole series wondering whether Tylor is that lucky or that good. I’ll also second The Hamster King’s suggestion of FLCL. It’s a mind-fuck of a series, but fun.
Other series I like that I won’t offer plot synopses for: several of the Gundam series range from good to awesome. In no particular order: Zeta Gundam; Gundam 0080: War in the Pocket; Gundam 0083: Stardust Memories; and Gundam Wing and Gundam Wing: Endless Waltz. Kishin Heidan. Ushio to Tora.