your family enjoys games, but has not taken the step into some of the longer Euro strategy games. (I'm not trying to disparage gateway games - they are fun and popular for a reason - just noticing that is what you listed.)

A critical question is how much time your group is willing to spend on a game. Dominion, Ticket to Ride, 7 Wonders, etc., you should be able to play in an hour or less. If you able to tolerate longer games, then it opens up a lot of games that involve more strategy and less luck. There are a lot of games in the 90 to 150 minute range that are really good. There are a lot of games in the 3-4 hour range that are very good, but those take a certain level of commitment that most kids, for example, do not have.

I steer clear of most games that exceed 3 hours, but a couple of my favorites push that to some degree.

I recommend going to boardgamegeek.com and looking at the game rankings:

https://boardgamegeek.com/browse/boardgame

The highly rated games are all good, but not all of them are good for all types of players.

The website is not very user-friendly, but you can click on any game and see something about the game (estimated play time, mechanics, etc.), scroll down to the "video" section, sort by clicking the "hot" button on the far right and then you'll have some good videos that will walk you through almost any board game.

Some games I think would be a good next step:

Lords of Waterdeep (Don't be put off by the D&D theme - it has virtually nothing to do with D&D)
https://boardgamegeek.com/boardgame/110327/lords-waterdeep

Galaxy Trucker
https://boardgamegeek.com/boardgame/31481/galaxy-trucker

Age of Empires III (The board game, not the video game.)
https://boardgamegeek.com/boardgame/22545/age-empires-iii-age-discovery

Tribune
https://boardgamegeek.com/boardgame/30957/tribune-primus-inter-pares

Castles of Burgundy
https://boardgamegeek.com/boardgame/84876/castles-burgundy

El Grande
https://boardgamegeek.com/boardgame/93/el-grande