Re: RPG Board Games?
I’ve never seen or played a GM-less RPG. IMO, the simpler the rules, the more important it is for the GM to have control of the situation and being willing and able to adjudicate all of the oddball situations that come up. IMO pretty much any rule system can be fun and engaging with the right GM. It’s all about how well they can lay out the scenarios and often good storytelling is the key.
OK, that said, have you looked at the “How To Host A Murder” games? I think those fit most of your requirements, but I’ve never played one. As I understand it they’re basically canned mysteries and each player is given certain clues and they need to discuss things with other players to put the clues together and solve the mystery.
There are also some co-op boardgames out there if you haven’t tried them. They tend to be light on the role-playing aspect but require coordination between the players to beat the board. I haven’t played the D&D board game (nothing recent anyway) so I can’t say how good that is, but some others that I’ve played are Shadows Over Camelot, Arkham Horror, and Pandemic. They might be worth looking into.