Leaving aside the question of whether substitutionary atonement is true (and if so, what kind): I could see it still being fulfilled for korban, inasmuch as any sin against our neighbor is also (and even more primarily) a sin against God.
Another-but-very-closely-related line of discussion would be how Jesus’ remonstrance about attempts to be forgiven of sin against one’s neighbor without actually reconciling with one’s neighbor personally, should be construed if substitutionary atonement is true.
One feasible way, off the top of my head, would be if substitutionary atonement is true in an Arm more than a Calv sense, and so is only potentially not actually true for any individual (even at the level of God’s own eternal existence–although that would run against several pieces of scriptural testimony, which of course is why Calvs point those up to it being real and accomplished already) until that person accepts it. But (for various reasons) God does not count the sinner having accepted it until and unless the sinner attempts to reconcile (under the arbitership of God, of course) with his brother.
Calvs would say, with some real scriptural justification (and some real metaphysical justification, too), that any such atonement must already be a real fact by God’s own action, and so the only question is when (historically speaking) the elected person will seek to reconcile with the brother he has sinned against. (Assuming the Calvinist doesn’t dismiss such reconciliation as unnecessary under the glory of God etc.) A Calvinist could plausibly contend that the elected sinner would be chastised by God (not being spared punishment, but rather permanent condemnation), and omnipotently so, until he does what is right in regard to his sinned-against brother. But I don’t know that this fits the character of Jesus’ remonstrance, as it stands, which sure looks more like God is refusing atonement with the sinner in some significant fashion until the sinner repents and does right to his neighbor.
(While the warning doesn’t explicitly say that, either, there are other related warnings in the Synoptics which would seem to fit along that line: that unless and until we forgive, we ourselves shall not be forgiven–and even that what forgiveness was vouchsafed to us already may be revoked! Which would also synch with several chapters in the Epistle to the Hebrews. See also the immediately surrounding contexts to Matt 5:23-34, one of which has clear connection to the parable of the unforgiving steward: he who was forgiven but then who chose not to forgive and so was handed over into prison, from which he would not come out until he had paid up the final cent.)
So scripturally there are strengths to both positions on the topic (Calv and Arm alike): our atonement (‘substitutionary’ or otherwise) is a completed eternal fact and action of God (with us as the object of His action), not requiring us to earn our atonement, which is why we can be trustworthily assured that God will succeed in saving those He eternally acts to atone from sin; yet also in another way our atonement with God is not yet complete so long as we still sin against our brother (including refusing to reconcile with him–including searching for some way out of having to reconcile to the one we have sinned against).
A Calvinist can go with both options well enough, appealing to the distinction between God’s eternal action and historical events, typically exemplified in the common scriptural theme of “already/not yet”. But an Arminian, starting from a distinctively Arm position, could only go with both options by shifting to universalism; since one of the key Arm vs Calv points is that God acts, especially on the cross, to atone all sinners, not only an elected fraction. If God’s atonement of all sinners is actually real, however, not merely potentially real, then we can and should expect Him to eventually succeed in saving all sinners from sin historically.
Thus the tension between Arminian types (including non-Protestant versions thereof) over whether any salvation of ours is actually or only potentially real and if so how it can be shifted to being actually real, or only temporarily real and if so for how long or under what conditions; thus again the pertinent draw of Calvinism (including non-Protestant versions thereof) and its reassurance that God’s salvation is actually eternally real and so shall certainly be historically accomplished, no ifs ands or buts. (‘But’ only for the elect, not for everyone. 
Hopelessness has to be maintained somehow, or else they’d be universalists of one or another type! 
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