Apocalypse World was the first game that immediately clicked for me, as though it reached through the psychic maelstrom and spoke in the language of my mind. Vincent and Meguey are no shit designers and I love their voice in the rules text, conversational and evocative but frank. I love that the game trusts the players and encapsulates all that they need to know about their character in a playbook, all that they need to know about the world on the move sheet, and it elicits everything else through play. I love that the MC has procedures to govern and support their role at the table. I love the way information is structured in the game - the modularity of the moves, the hierarchy of moves/principles/agendas. I love how powerful language is in the game without taking away from the numeric mechanisms.  I love that the game-as-conversation works so, so well across formats from face-to-face to play-by-forum. I love that the game was meant to hacked and that the designers supported those endeavors in the text (and in person). I love how Apocalypse World pushes and pulls and seduces and manipulates you into the post-apocalyptic genre and how each of its hacks suck you into theirs. I love how mature the game is, how it demands humanity from you even in a world of scarcity. There is so much to love.

An obvious way to avoid high fantasy and silliness is to tell your players, up front, that you're shooting for serious low fantasy.  The rules are really robust and you can totally play DW as serious fantasy.  Just ask them to support that tone and occasionally remind them.  Also, make harder hard moves, make them make harder choices.  Don't put their happy kingdom in peril, give them a chance to evacuate some children from their occupied ghetto.

There was a DW supplement for doing Diablo called Poor Tristram.  There was also a D&D3E Daiblo supplement that might make a good reference and starting point for conversion.

Bonds wipe at the end of the session.  Always write bonds anew with the characters present at the beginning of each session.  Any continuity is on the players to maintain.

Yes, you still get XP for failing but I've found the advancement to be just right.  You could always increase the number of XP required to level if you thought things were going too fast...

Make them try it and defy danger but perhaps go with soft moves...

Just think how much damage a 2-handed bow could do!

Easy hack, at the end of the session, add the question "Did every character do something awesome?"  If the answer is yes, everyone marks XP. 

Or

Put some tokens in the middle of the table.  Whenever you think someone else does something awesome, give them a token.  At the end of the session, tokens may be spent, 1 for 1, to:
- ask another character a question
- have them ask you a question

The former is less bookkeeping, fits within a preexisting mechanism, and has a token impact on the XP economy.  The later rewards excellent input into the game with some time to bask in the spotlight or shine it on someone else.  It also lets you have a couple in-character asides at the end of a session where characters can share thoughts, feelings, intents, or backstory.