Tsuro is a very quick, Zen game. It's tile placement and stone movement.
Obviously if you don't like S.H., you probably won't like The Resistance or Avalon. But from the same publisher, there's Coup (a game of creative lying), and Grifters (an engine-builder made up of resource collection with a crime theme). I like them both and they're very quick.
I don't think Fluxx could lead to long term frustration, because it's just so wild.
Catan is a classic and it's never caused tempers in my group.
It's a really fun game - and if you want a more typical action-RPG vibe, you should also seek out the Genesis Shadowrun game. The games are very different, but both are true to the Shadowrun experience.
I tried to avoid translations in my list. But anything by Aeon Genesis is also great, so is Mother 3 with the Tomato Ring. The SMT translations are a high point too.
Hands down my favorite lately is Shadowrun (SNES) - the addition of SNES Mouse support. It makes the game so, so much better. That's been huge for me, since the game is a point-and-click adventure. It's such a quality-of-life improvement. If the mouse existed and was common when Shadowrun was written, I have to hope that they would have thought to allow it.
Also, obviously there's a huge community of SMW hacks, and pretty much anything well-reviewed on SMW Central, I'm liable to enjoy.
In line with yours, there's Pokemon UItra Violet, a great hack of Fire Red for GBA. Also Pokemon Naranja, another Fire Red hack that's based on the Orange Archipelago.