Burning Wheel has everything you want in this, really. Its heavy crunch with a good amount of narrative mechanics, high on tactical decisions (more so than D&D, in my opinion), has equal support for physical combat and social engagements, isn't class based, character advancement is organic (using skills improves them), magic items are rare and interesting but not more important/powerful than your actual character's skills, spellcasting has its place but isn't gamebreaking, and so on.

And, I guess just tell them that. This game isn't your typical hippie lovefest like Primetime Adventures. You will have to make legitimately hard mechanical decisions. More than you ever did with D&D. The elegance of the game is that it will take your drive to play optimally and turn it into compelling storytelling whether you intended it to be that way or not.

If you try to go in and play a "Kick down the door, kill the orcs because they look different than us, loot the bodies, get XP, and now lets go find bigger orcs" sort of game, you'll end up getting it, plus accidentally telling a much more awesome story on top of it. Just, effortlessly. It will just happen, independently of your group doing anything to make it happen.

(If you actually try to tell an amazing story - good lord.)

Its hard to explain. But, having been in a similar situation, I'm confident that if you can get your group to just stomach it for a session or two to get over their "OH MY GOD IT'S NOT D&D" attitude, it will make everyone happy and solve all your problems.