Does anyone have any recommendations for games where I can just wander in circles, kill enemies in turn-based fashion, earn experience and gold, and just relax while slowly leveling up my character?

(I would prefer no random drops. I would also prefer no isometric or 3D. I also prefer it to not have random stat growth.)

that's one of my favorite gameplay loops in all of gaming.

Super Saiya no Densetsu?

Legend of the Super Saiyan

Artifact Adventure and its ilk. Fun games. I love them at least.

I do not own a 3DS because of DRM issues, and have no plan to get one (*maybe* after Nintendo stops support, so that if I want to hack it I don't have to worry about exploits being hacked or risking being banned from a (no longer existant) online service).

PC games might work, though I think games released on cartridge-based home consoles, or on portable systems of that era, are probably better choices.

One other thing: The GBC version of the original Dragon Quest isn't as good for this purpose; they greatly increased the experience and gold earned from killing enemies, and as a result the game is much shorter. (This also applies to other remakes of the game.)

Try Breath of Fire on the SNES. That game has an insane encounter rate reminiscent of DQ.

Earthbound Beginnings (aka Earthbound Zero) on the NES is also a good choice and a straight DQ clone. It too is very difficult and suffers from maze-like dungeons.

I've played that game, and:
* It can be beaten without having to stop to level up.
* There's too much of a focus on dungeons, and not enough wandering around the overworld, fighting enemies for XP and gold.
* When you hunt on the overworld, the game turns into an action game. (With that said, hunting is not actually mandatory, but that still doesn't sit well with me.)
* The game tries to imitate Dragon Quest 4 with its party swapping, but doesn't go all the way; in particular, active party dead causes a game over instead of having the inactive party jump out.

(I am looking for a game where I spend most of the time killing enemies for XP and gold, not one where I spend most of the time progressing the plot or exploring dungeons.)

Titan Quest has been a lot of fun for me. Dunno if that's like Dragon Quest.

Looking it up, it's described as action, which is not what I am looking for.

It's not turn-based but definitely rpg, fairly similar to D&D, at least in some respects.

Fallen Enchantress is pretty decent, worth a buy on sale. And is turn-based.

It appears to be tactical turn-based; this means that I would have to pay attention to the location of each character in every single battle. I would rather not have that.

(Also, I would prefer not to have to make permanent choices when leveling up; simply choosing a class (or similar) at the start of the game is enough choice for this purpose.)

Only other thing I can think of is find a persistent world that's to your liking.

Maybe one of these games. Never played them, but they look like what you're looking for:

Cosmic Star Heroine
https://www.gog.com/game/cosmic_star_heroine
Pier Solar and the Great Architects
https://www.gog.com/game/pier_solar_and_the_great_architects
The Legend of Heroes: Trails in the Sky
https://www.gog.com/game/the_legend_of_heroes_trails_in_the_sky

Dragon Fantasy, NES design totally of the DQ likes.

https://store.steampowered.com/app/327980/Dragon_Fantasy_The_Volumes_of_Westeria/