and I liked how you told Lapis Lazuli’s back story, but the end is confusing. Where exactly did Rainbow-Hair and Fiery-Tail find the blue-haired girl? Were they in a void left by the deleted badfic? Was she running on a generic plain in Nowhereland? Did the same agents who had been assigned to the badfic coincidentally find Lapis in the corridors of PPC HQ?

His eyes went huge and he and edged away.
One "and" too much,

Then Ripper and Alex appeared next to the canons just then...
The repetition sounds weird.

...she asked to the canons...
I think this "to" should not be there.

...an important artifact to him.
Word order is my weak point, but "an artifact important to him" probably works better.

She thought of when she had travelled across miles of country over the course of a few days.
I would believe in her ability to create plot holes if this had either been "hundreds of miles" or "a few minutes"; about one mile per day isn’t really fast. Or is the plot hole supposed to cause her travelling too slow?

HG

I'm going to pluck a random example of this from the place I was at when I decided to write. This isn't a specially-selected example, is what I'm saying:

Lapis quivered in terror when Matt’s Dragonic Backlash sent Giga Bowser stumbling dangerously close to the group. The air shimmered around her again, but she stopped herself before she could escape through the plot hole. In the midst of the overly descriptive action, the disguised Pokémon trainer had begun to notice something.

“I’m a little disappointed that it took me this long to realize this, but… Did you guys hear something… off about the way the canons and the Stu were talking?”

“We were so focused on the scriptfic format we got ourselves into that we didn’t hear anything,” said Sarah. “At least I didn’t. I was too busy trying to reset the format.”

Cupid’s eyes widened a little, recalling how he’d gotten distracted while his partners were arguing. “While you ladies were squabbling and doing other stuff,” he mused aloud, “I noticed that all of the characters were saying their lines at the same time. It was a lot harder for me to notice who was saying what because of that, like so many voices at once.”

Sarah gasped. “I think I know why!” she cried. “The spoken lines were not given separate paragraphs!”

There's something really off about the way you write, and I'm trying to pin down what it is. On the first hand, there's lines like this:

In the midst of the overly descriptive action, the disguised Pokémon trainer had begun to notice something.

Cupid’s eyes widened a little, recalling how he’d gotten distracted while his partners were arguing.

I get a really strange vibe off that sort of thing. I think it stems from the fact that the narrated 'actions' are so... non-physical. You're telling us that Lapis noticed something, rather than showing us her reaction: did she raise an eyebrow? Was stopping herself a reaction to the noticing? Equally, you show us Cupid's action, then explain it. I don't think the explanation was necessary - I think it detracts from the narrative flow.

On the other hand, there's the dialogue. Example:

Sarah gasped. “I think I know why!” she cried. “The spoken lines were not given separate paragraphs!”

Imagine telling someone something, and hearing that as their reaction. It doesn't sound like speech; that's not how people talk. People talk more like this:

Sarah gaped. How had she missed that? Then her brow furrowed in thought. "And I think I know why. It's the Words - the spoken lines didn't get separate paragraphs."

Your line reads as if Sarah had to wait for a dramatic flash of lightning to backlight her, and was expecting the scene to end immediately afterwards. "We must enter the castle - and destroy Dracula!" Drama like that isn't realistic.

And thirdly... how did they not notice that every single spoken line in the scene was said at exactly the same moment? It seems like something you'd comment on at the time, not a mildly strange fact that you'd pick up on later.

I dunno. Just... go read over that scenelet again, in isolation. Can you see what I mean about it sounding... strange?

hS

It’s a bit late for beta reading. I should really check my e-mail more often.

...a small metal cubes with buttons...
Should be "cube" (singular).

...the agents heard the devices make some futuristic sci-fi-ish sounds...
Should be "device" (singular).

Another long paragraph later, Matt managed to drive Giga Bowser and Matt away.
Do I need to read the badfic to understand what’s going on there? Is Matt driving away with Giga Bowser or are there two persons called Matt?

...during which the agents reset their format reset as usual.
I’m not sure whether resetting the format or resetting the "format reset" is the intended action here.

"What’s this guy gonna next, stop a school shooting?" she asked.
I’m not sure whether Sarah intentionally skipped a word there.

Armed with this knowledge, the canons proceeded to attack and fatally injure Moriamaru. The canons watched and waited.
Shouldn’t this be the agents, watching and waiting?

The new mini leaped off the Stu and headed over to join the agents.
“No,” Matt whispered in total shock, before transforming into his beast form and flinging Windscar off of him.
What’s going on here? Isn’t Windscar the new mini who had already leapt off the Stu? How could Matt fling him off then?

...silently thanked her lucky stars and superheroes that she hadn’t been flung into a tree.
Sarah has superheroes? Who are they?

Sarah and Cupid both cried out in stark horror. The Dragon Chain had severed his partner’s right hand with a single bite!
Since the first sentence’s POV was Sarah and Cupid’s, the second sentence’s POV should better not be just Cupid’s; thus "their partner’s".

And yeah, the interlude following this mission basically my way of killing...
Missing word "is"?

Will the agents be in trouble because nobody charged Naraku?

HG

A couple things I noticed...

(First off, unless my Internet sources are wrong, the title character's name is written Inuyasha.)

"A few paragraphs of dialogue passed by, during which the agents reset their format reset as usual."
Uh...what? I think you hit reset one time too many.

"“Go figure that he’d show off his wonderful toys,” she grumbled."
"Go figure" is used for an event or situation that doesn't make sense (it's shorthand for "go and figure that out", according to Urban Dictionary). Since it makes sense for Matt the Gary Stu to show off his cool toys, use something like "And of course" instead.

More tomorrow, when I'm less tired.

I know I said you could borrow Alex, but I never got the chance to look it over to make sure he was in-character. Yes, I was too busy to beta read the whole thing, but common courtesy says that if you borrow someone's agent, you let them look it over before publishing. Not cool, dude. Way not cool.