This past year at work friends and I made a little board game and your complaints were our top requirements. We wanted it to be setup in minutes, explained in 5, played in about an hour, with turns lasting just minutes at most and with a high degree of social interaction and yet still have a fair amount of depth and strategy.
We ended making a little stock game called "Day Traitor" where on your turn you play one of your three cards that let you see the future of two stocks, followed by selling and buying stocks, and cash out for gold. Get 10 gold and you win.
The amusing part is that on the back of the card half of the information (either the stocks or the amount they will change) is visible so everyone else around the table can see this partial information. And to go with that you might have just bought a bunch of "Red" stock further leaking information that you think it will go up and so the person going after you might also buy Red. When you buy a stock it gets a bonus $1 bump in price (as well a negative $1 bonus when you sell). This all combines to create many situations where we try to convince each other the now is the time to buy/sell something to great amusement because doing so might help you. Over the course of the game you need to cash out for gold, but the more gold you buy on a turn the more expensive it is so you want to acquire gold at just the right speed for however the game plays out.
There is a little bit more, but that is the meat of the game. It has been a lot of fun designing it with our group and just need to get some art and then I will stick it up thegamecrafter.com or somewhere so at least we can get a copy. We went through a lot of design choices where we found something fun, but would cause a turn to take twice as long or double the explanation time or setup time. We ruthlessly would cut anything that didn't add fun or broke our requirements of fast quick setup and explanation and in the end created something pretty fun.