Hunter x Hunter

Re:zero is entertaining. It's got some layers to it. I wouldn't say it has time travel, but time is an important aspect of the story, which does lead to some "time travel" adjacent shenanigans.

Steins gate is good, that one has actual time travel, but there is a romantic overarching story.

Attack on Titan has almost that great, government is behind something shady and the protagonist is in the military so has the resources to find out the state's secrets that FMA has.

None of your other animes really focus on romance, but if you're feeling adventurous Clannad and it's followup Clannad: After Story are fantastic. Toradora is also pretty cute.

In terms of worldbuilding and characters, One Piece is amazing. I also recommend Attack on Titan, Steins;Gate and Gintama. Gintama is mostly a comedy show, but certain serious arcs rival best action anime has to offer.

You are ready. Watch JoJo

Actiony:

• Jujutsu Kaisen: probably the raddest one coming out right now in my opinion. Beautiful art and fight scenes. Great story.
• One Punch Man: Love it. Very goofy. Again great art and fight scenes. Just be ready to have watched everything out and still no 3rd season.
• Blue Exorcist: Classic boy finds out he has powers. Goes to a cool high school to train. I thought it was fun, plus I'm a sucker for supernatural stuff.
• Code Geass: Great story with some political intrigue. I think this is on a lot of people's top 10s.
• All of Gundam: If you want to get sucked into a whole world with tons of series get into Gundam.
• Deathnote: Fun cat and mouse thriller. Reminds me very much of Sherlock and Moriarty style cat and mouse games.
• K: First season is great. Unfortunately I couldn't get through the first episode of the second season. Maybe I'll try it out some other time.
• Castlevania: Follows the storylines similar to the video games. Just brutal vampire shit. It's great.
• Megalo Box: This one is amazing. Lofi hiphop vibes and a great underdog rocky style boxing story. Really gave me Bebop/Champloo vibes.
• Assassination Classroom: Weird concept. I didn't think I would like it but came to love it. Kids have to learn to kill their alien teacher by learning to be assassins.

Some non-actiony animes if you are looking to branch out that i've enjoyed are Saiki K, Food Wars (so fan servicey but a really fun story if you ever liked Iron Chef), Zom100 (I guess this is kinda actiony, but more fun), Mashle (again actiony, but more goofy).

I could probably list a million more but my list is getting really long. I also second the recommendations in the other replies.

Since the live action was recently released, might I suggest a classic? YuYu Hakusho is one of my favorites. Great characters and great story arcs. The Toguro and Sensui arcs are great. I think you'd be better off watching the anime before the live action though. It's the same author as Hunter x Hunter. You'll also notice how a lot of manga authors took inspiration from YuYu Hakusho (note the black hair, green outfit styles of the protagonist).

Probably not what OP is looking for, but I really enjoyed the Sand Land series' first season. Maybe I'm a sucker for that Akira Toriyama (RIP) style. I recommend it.

If you liked Inuyasha, check out Dororo

Gurren Lagann

Your list of anime tells me are into adventure anime or with heavy action.

First thing I thought of was Katanagatari, where our heroes go on a journey to collect 12 legendary swords.

Something with heavy action: Black Lagoon- businessman gets abandoned on a pirate island and joins them

something more adult: Vinland Saga- viking epic following a young boy on a quest for revenge

Two that just ended that I thought were exceptional are Frieren and Apothecary Daires. The latter better be anime of the year. I don't think either are considered Shonen, if that matters to you.

Frieren is really chill and explores the little time we have with the people we care about. The first episode tells how an elf spends 10 years with a party to defeat the demon lord. But now they split ways and time moved differently for our elf protagonist since elves live thousands of years.

The second is a masterpiece of a story. A girl raised an apothecary (someone who deals with poisons and medicine) is kidnapped and sold to the palace to take care of the emperor's concubines. She is so intelligent and is a problem solver. I don't want to give more away. I hope more animes have story telling like this in the future.

My favorites in general are Bleach, Yuyu Hakusho, Hunter x Hunter (2011) and FMA:B.

Edit: Sorry, I was looking for new communities and I didn't notice this thread is months old.

I'm surprised no-one suggested Demon Slayer! I think it fits perfectly in your list!. If you liked MHA, I guess you should enjoy Naruto ( if you didn't already)

I also definitely second suggestions like Attack on Titan and Jujutsu Kaisen (just started but already hooked up).

Other stuff slightly less adherent to your list: In terms of "grand well prepared" storylines, I really liked 7 Deadly Sins

If you like braniacs like Death Note, I strongly suggest Code Geass and season 1 of Promised Neverland (unfortunately season 2 goes to hell, but imo season 1 is still worth it)

Finally, in terms of world/atmosphere building, Made in Abyss is a jewel (but pretty intense)

From recent ones I can recommend "Jujutsu kaisen" and "Chainsaw man"