All things have their being by and from God. This is a restatement of the doctrine of omnipotence.
All things have their being in and by way of God: in him we live, move and have being. This is a restatement of the doctrine of ubiquity.
All things have their being for and toward God; he is the end toward which they tend, and that end is the reason of and for their being. This is a restatement of the doctrine of pronoia.
God is then the origin, ground and end of all things; and all things are therefore integral to his life, and partake therein, whether or not they wish to do so, or realize that they do. This participation in the life of God is the mode of their existence, for God is the being of beings. By this participation are they known to him, as aspects of his own life; by that knowledge are their acts of existence completed, for no act of existence is fully complete until it is known and reckoned by God. So the inception of creatures by God and their completion in him are aspects in the singular, integral act of their creation, of which their inception, evolution and completion are phases.
The integration of all things in the life of God is a restatement of the doctrine of omniscience.
By omniscience, all things are in their truest nature integrated into the being and life of God, and are thus – in their truest natures, mind, albeit not necessarily in the relatively defective natures of their creaturely actualities – rendered consubstantial with him.
What then is the nature of the defect in defective creaturely actuality? It is an error about our consubstantiality with God – about the fact that we begin, proceed and end in, from, by, and toward him. It is the illusion that we and our fellow creatures each subsist independently, and are therefore our own creation, beholden only to ourselves. Because it errs in regard to the true order of things, such vanity generates acts that disagree with reality, and thus inflict harm upon the world – sinful acts.
Conversion of the heart – known also as samadhi, moksha, metanoia, enlightenment, awakening – is liberation from our illusion of independent subsistence. It is our recognition of our fundamental epistemological error about our ontological dependence on God, and our agreement with reality.
Our participation in God is by way of our participation as creaturely actualities in his understanding of our truest nature. We participate in God by being wholly our truest selves – which, they being found realized only in him, we can do only by participating in him. And when we do thus participate, we do so by making the nature of our substance indistinguishable, and thus identical, with the nature of our truest substance sub specie aeternitatis. This is just to say that we participate in the Divine life by making our own life his – such is the motion of our sacrifice at the Mass – and surrender the determination of our own substantial being to his Will, so that our substantial being is consubstantial with that portion of his substantial being that is about us.
Spatiosissimus is accession to the Beatific Vision, by which in seeing God we shall see in and through him all things, sub specie aeternitatis. It is the apprehension of the ubiquitous reality of supersubstantiation – which if ever real, is real eternally.
Apokatastasis is then just the doctrine of omniscience restated in terms of the creaturely perspective.
The difference between the blessed and the damned is simply that the latter do not see – refuse to see – that they are at all only insofar as they are in God, and that they are therefore saved. Hell is slavery to the sin of pride – or rather, properly speaking, of vainglory. And the vainglorious prefer their vanity to the alternative.
So in Truth the redemption of the world covers all things; for Truth covers all things. But the damned, while beloved of God and preserved in being by him, do not choose to recognize him in and all around themselves, as the source and substance of their being, the being in whom alone they themselves have being.
The apokatastasis is then realized already. Hell is a department of the life of God, a mansion of Heaven; and since in Truth they are actually saved, the damned are such only in and for and by themselves, on account of their errors about the Truth and Fact of their salvation. They sit forever at the Wedding Feast of the Lamb, and count its wonders horrible, and themselves lucky to be potent to fast therefrom.
There is then no conflict between the doctrine of apokatastasis and the doctrine of Hell.
 “Independent subsistence” is actually a contradiction in terms, for “subsist” is “under, up, to” + “stand.” You can’t be both under or toward something and independent from it. “Independent subsistence” is thus “insubsistent subsistence.”