I think that definition of "epic fantasy" is pretty narrow - saying that one couldn't have an epic D&D-styled game, or that Final Fantasy VII or God of War don't feel like epic settings, does the entire genre a disservice (even though they feature mechanicals, oozes, and other no-nos from your list).
IMO, epic fantasy is more about stakes than it is about details. What happens in epic fantasy that does not happen in your average D&D game? Let's use for the sake of arguement 2 epic fantasies of the Western bent: the Lord of the Rings trilogy and the Odyssey.
* The stakes are high - the higher, the better. LOTR had the Fellowship being the sole force that could unite the powers and thus prevent the ultimate fall of all free peoples. Pretty big deal.
* The heroes have a preternaturally powerful talent, status, or fate. The heroes are marked for greatness - the Fellowship is made up of an ancient wizard, an exile king, 3 princes, a guy charged with the fate of the world...and 3 civilians for everyone else to relate to. Odysseus and his men were resourceful and held special talents that kept them alive and through creative appication, gave them an edge to tip the balance in their favor.
* The challenges are gigantic. Epic heroes might be world class, but their enemies are too - Sauruman, Sauron, Cerce, the Cyclopes, all were worthy opponents. The mooks - well, better send an army.
* The heroes change worlds, and their successes and flaws reflect upon the world around them. Every action - for good or ill - has dramatic consequences upon the story and the world around the heroes. Aragorn's forefathers' failure to reign in the power of the One Ring cursed man to ruin, and Frodo's gradual seduction by the Ring nearly costs the entire world. Odysseus's cleverness gets his crew out of many scrapes, but his hubris also costs many men their lives and many years at sea, as well as his kingdom (very nearly).
* Don't forget big setpieces. Travel, exploration of the unknown, clashes of armies - they are all critical to giving epic fantasy its epic feel. Odysseus' journey was entirely about facing the unknown and defeating it. LOTR send the Fellowship through dangerous areas and vast enemy forces to acheive their goals. For it to be epic, everything needs to feel big and important.
With those sorts of core themes, I think soe of the points that Catodon brings up (the lack of "joke" characters, the possibility that good might not win) become natural outcroppings of the campaign rather that flat restrictions. If the players feel the gravity of their challenges and what hinges on their actions, those will evolve to become part of the campaign. Speaking from personal experience, it's far better to create an environment where the players want to play that way, rather than tell them how to play your game.