Good cutaways jokes are 10% inspiration, 90% timing.  Keep the editing tight (especially if it’s cutaway dialogue and not just a 3-second Family Guy clip), and as long as it doesn’t overstay it’s welcome, and as long as you think it’s funny, it should work for your audience.

I must vehemently* disagree with you about the “need” for fantasy to be silly.  It can be silly, sure, but it should only be silly if it’s intended to be silly.  Fantasy just means a story constructed such that can’t happen in our world, so the audience has to stretch their imaginations a bit and imagine a very different setting, and perhaps some very different assumptions behind the characters’ actions.  But that’s no reason such a thing should be treated any less seriously.  Of all fantasy works, LotR was the MOST deserving of reverence given how influential a work it’s been for decades of authors, artists, and readers.  It’s not pulp to be read and forgotten, it’s not dated camp (like the old Star Trek inadvertently became), it’s not even meant to be a light-hearted, whimsical tale for children.  It’s intricate, it’s sprawling, it’s mythos.  It’s more or less the New Testament, Ramayana, and Iliad of an entire genre.

That doesn’t mean the movie requires slavish devotion to every event in the source material, but I think it does require that the story and it’s place in our world be taked seriously and respected as the creator intended and as the long-time fanbase expects.  You don’t have to include everything the author put in there, but you should not add new material that flies in the face of the author’s intentions or disrupts the story’s themes or atmosphere.  Fundamental changes to the plot or to major characters, lowbrow humor not featured in the original story, fourth-wall breaking references only relevant to our universe and not the characters’, I think it’s all very distracting.  The audience should not be taken out of the story by having the filmmakers shine a light on how goofy things CAN seem if looked at from the right angle.  Instead, those rough edges should be ironed out if possible.  If some element of the story doesn’t make perfect sense by 21st century Earth logic, then skirt around it, or, if you must, make a minor tweak that doesn’t fundamentally change anything important. That’s a big trick of adaptation, but anything worth loving is worth loving right.  If the story is meant to be comical, self-referential, or be a satirical take on the author’s world or on ours, that’s fine.  It’s ripe for adaptation and updating.  But Tolkien never did that.

The parts of the movies I don’t like were the parts where I was pulled out of the action and conspicuously reminded that it was all just a movie, and that only happened for me when the filmmakers stepped completely out of the story to set up a gag, introduce a film trope that didn’t fit, or made a major change to the story or the characters.  I realize I’m being inflexible and almost dogmatic here, but I think the Lord of the Rings is not only worthy of such reverence, but that it uniquely deserves it.  And Tolkien deserves some more zealots.

And to pick up on what Michael Novelli (bravely) mentions in his post above, about the Bakshi versions: while I can’t say that I agree with him on which is the better adaptation, I do think better of the Bakshi version’s shortcomings.  When that movie was bad, it was mostly due to technological or budget restraints or by edits necessary just to cut down the story to make it digestible for a 1970s audience that would have been even less familiar with the story and the world than a 1990s/2000s audience (Dungeons and Dragons was brand new back then!).  Jackson had no such limitations, so his additions seem entirely gratuitous.  He’s clearly been a fan of the books far longer than I have, but I do not understand why he, as a long-time fan, made some of the additions and changes that he did.  I have to hope he did so only reluctantly out of a belief the film would never have found an audience otherwise, but I can’t think of how any of these changes made the movie better or even more accessible.  With the exceptions of Arwen and the cliff scenes, the additions add nothing save a few instance of cheap humor.  There’s more than enough action, there are pretty visuals in every shot, he had a perfect cast lined up, and a gorgeous soundtrack seeping through every inch of the film…why shouldn’t that have been enough?  Edited for pacing (and for the unadaptable, like Bombabil), all you needed to make a great series of movies was already in the text.  The movies for me are still a gem; how often do you encounter a movie that’s 95% perfect and big and gorgeous and spectacular and unbelievable , etc.

But the last 5%…oooh, how that stings!

* – Yes, I’m using big words gratuitously because you’re foreign. :p