Nice idea but it has too many holes.
He was last seen with a woman named Ryuko Haname, his grandmother who he was taking care of because she was ill.
Wait. If his grandmother was ill, due to her age, I suppose she was at home. If he was last seen with her, that means someone must've gone to their house and saw them before Daisuke went missing. And if we know that fact, that means that that same person told us that fact. So, you should've included their questionings in your case.
He went missing around 3:30 that afternoon
How do you know the exact moment that he went missing?
If he left the home at 3:30 PM, that wouldn't mean that he went missing the exact same moment.
his body was found in an abandoned car
When? If he went missing, we need to know when was the body found so we can narrow down the places where he could've went and people that he could've came in contact with.
The victim had been stabbed once in the abdomen and shot once in the head.
As I've already said, if his grandmother was ill, she would be at home and cleared out of suspicion. The two remaining suspects are friend (male) and ex-girlfriend (female). If he was shot, it's logical to think that a male did it because female usually cannot handle a gun that well, except if it was a type of the gun that anyone could handle. That's why we need a capsule of the bullet, so we can find out what gun was used.
There was no clues at the crime scene except for a half-smoked cigarette.
I'm getting back again to what I first said. His grandmother was ill at home, and she was the only smoker. It's obvious then that the cigarette was either coincidentally there, or was placed there. But, if it was placed, what's the reason? To blame the only person that smokes aka his grandmother who's at home? I don't think so, which leaves us with only possible solution, coincidence.
Well, I think that's about enough for now. My purpose was to try and give you some leads with this post on how to fulfill some of the holes. Hope it'll be of some help.
If she smokes at her age, it probably means that she's a heavy smoker. For them, even if they're on the verge of death, they won't stop smoking, so it wouldn't be unusual.