Short version
I don't think Abe believes a Friday morning exit from a "future Abe" is possible.
The Abe hatching this plan already has (thanks to the phone call paradox) what he considers sufficient evidence to invalidate the "single timeline" model, in which causing a paradox will cause a disaster because there can be only one version of history. He wants a controlled experiment to see if what happens will fit a "diverging timelines" model, in which travel backwards in time either generates or allows access to independent "offshoot" versions of history.
He may also believe that the future does not independently exist as a causative agent that can impact the present, because, despite his own experience as a time traveler, he has not yet encountered anyone that he recognizes as "from the future."
Thus the plan makes sense to the Abe on-screen in that scene, though his model of what's going on with time travel likely differs from the one you used in composing this question.
Long version
Your question is slightly confusing because of the way you're using the parenthetical notation to designate individuals. Most people using this notation use the number in parentheses to indicate the number of trips back that individual has taken. Thus, when you say:
- Thursday 17:00 - Abe(0) exits machine having just punched Platts.
- Friday 2:00 - Abe(0) scares kids preventing Abe(1) from waking up.
this would by the typical convention be written as:
- Thursday 17:00 - Abe(1) exits machine having just punched Platts.
- Friday 2:00 - Abe(1) scares kids preventing Abe(0) from waking up.
since Abe(1) is the one who has come back through time on this particular cycle. I think this may be causing part of your confusion.
Note that the Abe hatching this plan is not Abe(0) in the absolute sense, since he has traveled back several times already by this scene. Perhaps it is better to reference them with relative numbers, like:
- Thursday 17:00 - Abe(N+1) exits machine having just punched Platts.
- Friday 2:00 - Abe(N+1) scares kids preventing Abe(N) from waking up.
Adjusting the notations of Abe(0) and Abe(1), and replacing the absolute numbers with relative numbers as above, I think the schedule you're proposing looks like:
- Thursday 17:00 - Abe(N+1) exits machine having just punched Platts.
- Friday 2:00 - Abe(N+1) scares kids preventing Abe(N) from waking up.
- Friday 8:45 - Abe(N+2) exits machine having just routinely gone back.
- Friday 15:15 - Abe(N) enters machine ready to go back as is routine.
So you can see the fault in that you have N entering a box Friday afternoon but N+2 exiting that box Friday morning. Even if this is not a true fault, your proposed schedule looks like a faultily-reasoned scenario to the Abe doing the planning, as I'll try to make clear below.
First, let's review the dialogue from this scene:
Abe: Well, we can do this, but we have to do it now. Do you have his home address?
Aaron: Why now?
Abe: We were planning to take a trip tomorrow, right? Just like today?
Aaron: Yeah. For stocks.
Abe: Ok, well, half an hour ago, I was asleep, and this car alarm woke me up. These kids were down, skating by, hittin' every car on the
block. So... we go right now, do our business with Platts, get back in
the box, and come back to right before those kids are settin' off the
alarms. All we-- all we really have to do is stand there in plain
sight -- it should scare them off. That way my double sleeps through
the night, uh, they don't have the conversation we're having now, and
they get in the box tomorrow as usual.
Aaron: (pauses to think) Yeah. They'll be changed, but...
Abe: Yeah, but at least they'll get back in the box.
Aaron: Wait -- how do we go back that far, if the machines haven't been running? (pause) Have they been running?
Abe: Yeah. I, uh, started going by at five o'clock and turning them on -- 5 PM. I just got tired of the whole unanswerable quest--
Aaron: (interrupting) Are we doing this as an experiment, or are we doing this for me?
Abe: (pauses) A little of both.
I don't think that the Abe(N) hatching this plan expects to have Abe(N+2) coming out of a box on Friday morning. Remember that this Abe(N) has not yet been surprised by someone coming out of a box without it being part of his plan. If that scenario has already occurred (because Aaron used a failsafe), this Abe(N) does not know about that yet.
Also note that Abe(N) is being pretty daring here: planning to deliberately break symmetry with their "doubles," which is something he never wanted to do before. In all likelihood, this is because the universe continued to exist with no apparent ill effects after the paradox phone call incident (where Aaron's phone rings both the "first" and "second" times through a particular day) somewhat earlier.
It seems clear that, because they survived the phone call paradox, Abe(N) believes (correctly or not) that, after he's gone back and scared off the kids, his double will be not actually be Abe(N) (i.e. the true past version of himself, the himself planning now) but more like Abe(N-1') (i.e. some "other" independently-existing Abe diverging from his own personal historical frame of reference). In all likelihood, he has deduced that the Abe in the hotel when Aaron got his phone call the "second" time was similarly an offshoot "other" version of his past self. However, he noted that, when the afternoon rolled around, that offshoot got into the box and exited the timeline, leaving him as the only Abe in his current timeline.
Abe(N) knows that the "other" Abe (the one still in the hotel after the phone call incident) must have gone "somewhere else." It doesn't really matter whether that offshoot Abe evaporated or went to a splinter timeline inaccessible to the Abe(N) we're talking about here. He's gone. He's not contesting Abe(N) for control of his "life" (i.e. apartment, job, etc.) in this timeline. Abe(N) only knows only that his immediate situation appears to be functional from his current perspective.
Abe(N) expects a similar train of events as a result of his plan. The important thing to recognize (as the viewer) is that Abe(N) is no longer thinking in terms of absolute timelines but relative timelines. He recognizes that the relationship between an Abe(N) and an Abe(N+1) is NOT the same as the relationship between an Abe(N-1) and an Abe(N). He's been Abe(N), and he's seen Abe(N-1) while he was Abe(N). He's never seen Abe(N+1) [or anybody X(N+m)!] when he's been Abe(N). (Though this will shortly change with the Granger Incident.)
So Abe(N)'s thinking is that the schedule will be:
- Abe(N) (his present self) heads off to punch Platts along with "his" Aaron.
- His present self and his buddy Aaron come back to the boxes and use them, going to a new timeline containing an Abe(N-1) and an Aaron(N-1) -- with this "local pair" not really being their own past selves, as he knows now.
- His future post-travel self will prevent the kids from waking up that Abe(N-1) in the new timeline. Symmetry will be broken. Abe(N-1) (the past self he will remember, the one doing the planning now) can not possibly be the same as Abe(N-1') (the one who will be sleeping peacefully through the night in the new timeline).
- His future post-travel self (plus his buddy Aaron) will steer clear of the N-1' pair until the N-1' pair gets into their boxes the next afternoon. The N-1' pair will be going "somewhere else" -- wherever that may be.
- This Abe probably thinks that nobody will have come out of the boxes the next morning, because he no longer believes that there is a single unified timeline such that is required to preserve causality. He is obviously already thinking that causality is not something that must be preserved, as demonstrated by the fact that he is prepared to carry out the Platt-punching experiment in the first place.
As you can see, from this perspective of thinking, your question:
...wouldn't them getting in the box at 15:15 mean that they also exited the box earlier as well?
implies an identity between the individuals exiting/entering the boxes that the Abe in this scene would probably not agree is truly an identity.