I'm focused on the "laid back" part because, by definition, at any TS restaurant in WDW you will sit down and enjoy the atmosphere. There aren't any that I can think of that really shouldn't exist because it fails at its primary mission. The closest is probably like Rainforest Cafe -- I don't know if anyone would shed a tear if that one closed up, but even it has a cult following of picky 5 year olds.
I would look at the moderate and deluxe resorts that are not in the monorail loop. Nothing is guaranteed to be laid back at WDW, but those are going to be your best bet. Whispering Canyon at Wilderness Lodge, Olivia's at Old Key West, Sebastien's at Caribbean Beach, and Flying Fish on the Boardwalk can be good choices.
In the past, we have also really enjoyed Ale & Compass at Yacht Club, Boatwright's at Port Orleans, Story Book Dining at Wilderness Lodge, Sci-Fi Dine-In Theater at Hollywood Studios, and Cape May at Beach Club. Any are going to be hit-or-miss as far as crowd, but none are likely to be the equivalent of a "Be Our Guest" style craze.
While it's not laid back, we also love Biergarten in Germany at EPCOT for the atmosphere. It's a lot of fun if you are into that sort of thing. Like a lot of TS at WDW, the food is kind of boring, but not bad. It's also a buffet, and people dance to the music, so it might fail two of your three asks.
Enjoy your trip! The planning part is so much fun.