Here's a speculative scenario if KM is dead, if JC did it, if it was pre-meditated, and if he's a little smarter than he seems:
He discovers something about KM he doesn't like at the end of July, either unwanted attention (male boss taking photos of her looking beautiful) or her doubts about their engagement or the move to Colorado. He goes silent on Facebook from July 27 until after her disappearance... no more lovey dovey posts, no more cute couple photos.
She gets off work Saturday evening and he comes over to her place. After nightfall, he persuades or lures her to an outdoor secluded site, where he harms her and disposes of her quickly and effectively - maybe pushes her off a cliff or high bluff over the river? At any rate there's no evidence of defensive wounds on his arms or face when he physically appears for media interviews soon thereafter... so there couldn't have been much of a struggle.
I'm thinking her body could be in water or down a deep ravine or at the bottom off a cliff, since she hasn't been found yet. Or, maybe it was simply dumped not far from a road, and just hasn't been found due to bad luck.
He takes her phone, purse, keys, and goes back to her apartment. There is nothing to cover up or clean up since nothing happened in her home or their vehicles. He composes himself and comes up with or perhaps re-thinks what to do next.
Around midnight, he leaves her purse and keys at the apartment, takes her phone with him, and goes to a friend's house, quite possibly within the same cellphone ping radius, which for all we know is in the same radius as her townhome. He may even have had prior plans with that friend, thus choosing a night with a pre-made alibi.
At the friend's, he lights up and calms down, then texts KM's phone to tell her the documents have been burned. (Assuming they're real and that's really what he burned and that there was really a fire.) Then he surreptitiously answers himself from KM's phone - perhaps while in the bathroom, or in the woods for a wee if the friend's place is rural, or even just while stepping away from the firepit.
In the dark, from a distance of a few feet, no one would notice he's not texting from his own phone - he'd just look like he was texting. He wouldn't even have to go out of sight. He could just wander around, near or far from the fire, and slip the correct phone from his pocket at the correct time, and appear to be innocently texting.
After a couple texts back and forth, he looks through the pics stored on KM's phone and chooses one to send as the last text. Then he turns her phone off, and/or GPS off, and/or removes the battery. He then "receives" the pic on his own phone at 12:52, which is 7 minutes later or not, depending on if her phone was turned off at 12:45 or just "around" 12:45 - I don't think that was ever established.
Maybe he even shows her picture to a friend he's standing next to ("look what she sent me, doesn't she look pretty"), to establish with a witness that KM's in communication with him and they're not fighting.
He goes inside at the friend's house and watches TV, or doesn't watch TV, or he's 22, or he's 23, or or whatever. Leaves the friend's around 2 am. He easily disposes of her phone and the battery in any of a thousand possible places where it may never be found again. Then he goes home and goes to bed.
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Something like this same scenario could happen if it WASN'T premeditated - if there was a fight, then a crime of passion or even an accident. Only in that case I'd think he'd be too disordered and distraught to coolly handle a visit to a friend's and the reasonably clever smokescreen of the texting exchange.
Then again, I know exactly where to go if I wanted some xanax, valium, klonopin, or anything else to keep me calm - I'd go to the people I know in their young 20s who work restaurant jobs. Talk about a black market pharmacy.
Just thinking aloud.