I think we've gotten a little far afield from the original timeline! We don't know for sure, but the two girls and Emma's mom were probably all killed overnight on either Mon/Tues or Tues/Wed nights or early morning. Emma's dad came out to check on the house on Thursday afternoon (this is pretty well-timed). A single local police officer came out to the house at around 11 on Thursday evening to check up on things in response to the call from Mel's mother. An hour later, near midnight on Thursday evening, Sam called the police himself and two officers came out and checked the basement:
Yes; Emma's dad was already dead by the time of both police visits (which were separated by only an hour or two). Four hours later, Sam had to be pulled from the ditch on Poorhouse Road; the tow truck driver dropped him off downtown and he had breakfast before calling for the ride to the Richmond airport.
I like simpler theories more than complicated ones (Occam's razor). Sam got mad and killed Emma and Mel. Then he "had" to kill Emma's mom to avoid getting discovered. At this point, he doesn't have enough money to get to the airport (without a car; and perhaps Emma's mom has the van keys hidden or locked away to prevent joyriding) and also pay a change ticket charge. (He's not the most sophisticated of kids, and may not understand or have overdraft privileges, know about flying standby, etc.)
At this point, I think he's a freaked out and scared kid who realizes he's done something very, very bad but has no money and no plan, beyond a return ticket that he can't use until Sunday morning. It's really only a day or two between time of the first three murders and Emma's dad's arrival; but, after killing Emma's dad and hearing phones in house ringing (the calls from Mel's family), he just gets more freaked out and scared - though still able to turn first officer away with a calm enough explanation about the girls' absence to avoid having first officer enter the house, ask for the mother, etc. But, now he's more and more freaked, is hearing noises, and perhaps just calls the police out of real fear - of what, he doesn't really know (c.f., Dostoevsky's Crime and Punishment).
Shortly thereafter, he realizes that he might be able to find Emma's dad's car keys and use the father's car to get to the airport. Still no real well-formed plan, but at least he's on his way out of town. Unfortunately for him, it's a dark night (no moonlight whatsoever, new moon that month is Friday 9/18) and he is an inexperienced driver on dark and unfamiliar roads. He makes the bad turn off 460 onto Poorhouse, realizes his error after a mile or so, tries to turn the car around and gets stuck in the ditch. He could have been in the ditch by 2:00; that could have triggered the suspicious vehicle call, while still taking awhile for someone to notice the car, call police, and police and tow truck to arrive.
This is how I read what we know so far ...