The economia issue is a very difficult to wrap one's mind around for many reasons.
If you look at the most ancient sources, the assumptions (or perhaps we should say, the lack of assumptions) underlying St.Cyprian's view is what was universally accepted. By this I mean, the Church that Christ established is singular - one Faith, one Baptism, one Lord. This is what was revealed to mankind and given by the Apostles. There is no "runner-up" ecclessiology established by God; there is no single, neat clean way of describing the relationship of schisms and heresies to the Church. The whole business of how to reconcile those individuals or communities coming away from such ruptures is one of "picking up the pieces from the floor" - the Church is cleaning up a mess in those circumstances, and is left to decide what will be glued back together, what will be discarded and what will be replaced. Seen from that perspective, it's foolhearty to believe there is always only "one" possible way of doing this, save outside of the pragmatism of policy as established by a single local Church (ex. "we, the Holy Synod of (blank), receive converts from (blank) schism via this means"), and even this may not have a permanent character (depending on how the relationship of the particular schism to the Church changes).
I think what you can glean from all of the various canons relating to this topic (whether local or universal - interestingly, when it comes to the western heresies we are now most familiar with, there have actually been no universal/ecumenical canons formulated, but rather various local policies based in turn upon parallel situations dealt with by the Ecumenical Councils), is the following...
- the Church presumes nothing about the heterodox, in terms of refusing to affirm anything about them but recognizing that all speculation aside, such things could only be known to God.
- OTOH, the Church has recognized that not all schisms/heresies are undifferentiated amongst themselves, and even less, are not regarded as undifferentiated from infidelic religions and paganism, in terms of their relationship to the Church. What we can know, is that this is because at the very least, on the surface these schisms/heresies have certain key aspects of the truth which pagan religions do not...though certain grotesque heresies are treated, for all practical purposes, as paganism (like the gnostic heresies, or in modern times, something bizarre like Mormonism.)
We can speculate endlessly about what God may or may not do - after all, He is sovereign and will have mercy upon whom He will. We trust God, know Him to be good, and that He will not deal with anyone unfairly - if there is a lack of fairness, it will be because He has been gratuitously kind, not giving us the hell we all have richly merited at one time or another. But in the end, such speculations are just that - thoughts, and if anything, can be a cause for falling, like so many endevors into "speculative" or "creative" theology. Indeed, such activities in a real sense are more the realm of philosophy as classically understood, and not theology proper as understood by the Holy Fathers. It was by such speculation that western Christendom "jumped the shark", and if you look at the major heresies, they were instigated by such speculations and "what if" scenarios. Arianism is Christology straight-jacketed by rationalism; so too, in it's own way, are the other Christological heresies condemned by the Ecumenical Councils. Etc., etc.
Really, properly speaking, we ought not to even presume our own salvation, our own "perseverence to the end" - and that is speaking of those in the Church, with access to the truth, the Holy Mysteries, etc. Seen in this way, it becomes even more obvious that presuming things about the heterodox is really out of place, since their situation is far more dire.
One of the big mistakes (and it's been pointed out by many far, far wiser men than myself) of the ecumenical movement has been the idea that the Sacraments are somehow the "foundation" of the Church, in particular the Sacrament of Baptism. As Metropolitan Hierotheos of Nafpaktos has rightly pointed out, Christ is the foundation of the Church - in a real sense He is the Church, with men priveleged to become members of Him. Viewed in this proper context then, Baptism is not the foundation of the Church, but something the Church does to bring fallen men inside - it's the beginning of the assimilation of man into Christ. That's an important consideration, because the contary view portrays the Sacraments as autonomous forms, which given the right ingridients can be "confected" anywhere by anyone. It is only with such a way of thinking, that one can avoid seeing how obviously mistaken the presumptions of so called "ecumenical ecclessiologies" in fact are. Indeed, far from being fanatical, it actually makes a great deal of sense to operate under the basic assumption that once you leave the canonical boundaries which the Church has established for Her own self governance, you're outside of the Church. It's the weird "hocus pocus" type view aped from Roman Catholicism which is "weird."
As for the issue of "lay Baptism", this is a case of leniency within the Church. Should the person so Baptized live, one of two things can happen - it will be recognized, and the rest of the rites of initiation will be completed by a Priest. Such a view accepts that it's very likely such an act of liberality taking place within the true faith and within the Church (in an emergency) is honoured by God, and if perhaps it was not, the rest of the rites of initiation, Chrismation, Holy Communion, etc. will complete/fix what was wanting. However, it is not at all uncommon that for the peace of conscience (not only in regard to the individual in question, but also others they go to Church with who may learn of their situation) an exacting approach will be taken, and the person in question will simply be given ful, canonical Baptism by a Priest. The same is particular the case where circumstances force a frail person to be given Baptism by pouring water thrice over the forehead due to their frailty - if they recover, they may very well be simply given a full, proper Baptism for the same reason. The reason for this is simple - because the form of Baptism given to us by God, and promulgated by the Holy Apostles, is one administered by the Priest (who acts with Christ's authority, in His Name - hence "baptizing in the Name of the Lord"), with three immersions, etc. Anything less than that can be "repeated" - or better put, anything less than this can be ignored.
The Russian practice in these matters is quite liberal (and I don't mean that in a negative way), and that liberality was born out of circumstance - the Slavic peoples (not simply the Russians) came to live in societies that were often pretty "pluralistic" in terms of there being a strong presence of heterodox in their midst, or circumstances provoking schisms which were often beyond the control of "the little guy" (like the various incursions of Uniatism.) Given those circumstances, such liberality was generally well warranted - the Church doing whatever it could to avoid confusing the "little ones" and certainly having no desire to humiliate people in those situations.
OTOH the Greek practice became increasingly "stern" and "exact", because the above situations generally did not exist, and because the manner that the heterodox westerners were making attempts upon the faith of Greek Orthodox Christians called for a very clear, unambiguous witness to the fact that Orthodoxy is one thing, heresies are something else. It also didn't help that by the 17th century, the Latins (and most of their Protestant offspring) were universally practicing "baptism by pouring" as something normative. Though in the Ecumenical Patriarchate this has been softened a great deal, in Greece itself (which is independent, being under the Archbishop of Athens) and on the Holy Mountain (particularly the Holy Mountain) this exacting practice is still in tact.