With the disclaimer that I haven’t watched much anime, or seen any if the ones you mentioned. So I may be way off here but…
Since you mentioned the early 2000’s and based on the directions in stuff you may like.
A couple of later 90’s early 2000’s that fit
Gantz
Serial experiments lain
I second Lain
I was almost surprised nobody already mentioned it and and see it in the previous post 
The sound in Lain is amazing. Scenes with just power lines buzzing, amazing anime.
10/10
Also, probably one of my favourites and genuinely think you will like it based on what you like so far:
Boogiepop Phantom
10/10
Also, it goes without saying, watch it in Japanese and subs or don’t watch at all 
Just watch Primal on HBO. I think a lot or most anime is kinda silly but loved that show.
Ghost iIn The Shell and (almost) whatever by Miyazaki.
i myself am absolutely indifferent to that anime thing – but love these.
that’s from genndy tartakovsky right? the samurai jack creator?
you can’t really go from zero to boogiepop, you need several degrees of acclimation before that or lain will sit right with a person. I like those a lot also, however.
Yes… it’s like a Saturday morning cartoon for adults vs cartoons for tweens watched by adults.
I think I’ve seen a trailer once but didn’t get to see the series, love his work, need to make time to see it
I tried to watch Samurai Jack after but couldn’t get into it. Primal is like Captain Caveman with brains being squashed out from stomping but is rather touching as well. It was a very surprising experience for me…
he did bunch pf other stuff as well, I think he also did dexter’s lab which I loved at a time
Ghost in the Shell sparked my appreciation/interest for the genre in the past. Superb at every possible level.
Yea, I liked that as a kid as well… but like a lot of stuff it’s a bit of a mistake to revisit in my opinion. Like if I tried to watch Starblazers now not wearing an onesie it would just feel weird. Which makes me wonder… are bronies still a thing?
Used DT came with Pokémon samples onboard which I immediately mangled right up.
So I would like to think they only used one sample source for this device
if that’s true my world view just got a little bigger.
“Jin-roh: the wolf brigade” may be interesting for you, based on what you described
And this may be out of topic, but “Battle angel Alita” comics may interest you too. Anime and movie based on it do not translate the dark and cyber-punk atmosphere of the comics.
Same for Akira, that you mentionned: the comics goes way further than the already great movie. It changed my life in some way.
vampire princess miyu
has some of the same voice actors as neon genesis evangelion. miyu is maya from nge, misato’s voice actress is in one later episode. shinji’s voice actress plays a cute little monster thing. vampire light-horror anime with japanese style twists and turns, melancholy tone. great music by kenji kawai who did the ghost in the shell ost. stories are thoughtful. one episode depicts a lesbian relationship which i thought was pretty cool for a story from 1997. the first episode is so different in tone to the rest of the series so if you didnt enjoy the first ep keep watching 
One of my favorites, but Satoshi Kon in general are top tier, you just have to love twisted stuff.
Of course the myazaki films.
But Never…Never watch Grave of the Fireflies
If you liked Akira, Spriggan is a must.
The best of the best. However:
Berserk (original series)
Perhaps my favourite anime, along with Bebop and Champloo. Quirky, violent, oppressive, dark and leaves a lasting impression. The newer series delves much further into the manga, but does so at the cost of the animation, which sucks. Still, Berserk is a masterpiece.
Fullmetal Alchemist: Brotherhood
Even better than the original FMA anime. Heartfelt, deep and just a masterpiece in every respect.
Tengen Toppa Gurren Lagann
What a great show. Beautiful artwork, crazy action and a really deep story. Another work of art.
This sounds amazing. 
