I think it is an anachronism to refer to non-Ephesine Nestorians at this time. The issue was, and should be, Theodore of Mopsuestia. Ibas was his disciple and was circulating his materials. I think that had Ibas been alive a little later, and sought to be admitted to the non-Chalcedonian communion he would have been received by prayer and confession and the rejection of error, and as a bishop. This was the documented practice of the Orthodox Church of Alexandria when the division between the ACE, EO and OO had concretised.
I think that the Fathers of this controversial period did not believe, essentially, that adopting an error led immediately to losing all grace. I think this is a later view, even a very modern view. When we read in the Histories of those monks who had adopted a rather physical view of God, which was certainly error, they were not treated as those who had lost all grace and whose monastic enterprise was utterly repugnant to God, but as those who needed correction in love so that their effort might be more properly directed.
Likewise all of the schisms which took place in those times and during the first millenia. I cannot think of any occasion when the other party was considered to not be the Church at all, allowing for intemperate polemic. We see this in the fact that even after generations of schism such groups were reconciled without baptism or chrismation.
When we start insisting on Orthodoxy being essentially a matter of accepting the right propositions (and you know how much an accurate theology matters to me) then we rapidly end up in tiny groups calling themselves the Last True Genuine Really Orthodox Church. I mean that there are members of even my own Coptic Orthodox Church who I consider to be in error on serious matters, and even to teach error. But I do not rush to assume they have no grace, far from it, since I know that I sin in a hundred ways each day and am much more worthy of being abandoned by God as a fruitless vine.
Yet, when the Church deals with such error, as she must, it is the response of those who are in error which perhaps determines how they are received. If the person or movement accepts correction in love, and we must correct in love, then they are reconciled and we see the working of grace not the absence of grace. They were those who are Orthodox but held error.
If they reject correction, and worse, seperate themselves in schism, then they are, I believe, still Orthodox, but Orthodox not only in error, which is bad, but those who are in schism, which is worse. It seems to me that it is this schismatic spirit, which is not the same as genuinely being convinced of error, which is understood by the Fathers as being poison, and which from St Ignatius of Antioch onwards has been resisted.
It was not that Nestorius was a teacher of the views of Theodore of Mopsuestia which was the gravest problem, though do not doubt that I consider that serious. But these views had been around for a while. It was that he would not receive correction.
I am saying this because I am suggesting that in a community such as the Chalcedonians in the early period, what was significant to the Fathers was not that they had held error, that could be corrected, but whether or not a particular person persisted in what was essentially schism. I mean the separation from those who are also Orthodox Christians. When a Chalcedonian came to the non-Chalcedonian community he was both rejecting schism (and most people just found themselves in situations by birth or circumstance and were not deliberately schismatic on either side), and he was confessing the truth and rejecting error.
By the time of Constantinople II, but already in the Henotikon, and in the various conferences that had taken place, it was clear that most people on both sides believed the same thing. But they had different views about what Chalcedon and the Tome meant, especially as these became totemic.
I would not expect clear statements early on about the EO eucharist. But St Severus writes about those who commemorate names that he would rather were not. He insists that this does not corrupt the eucharist when the faith is pure. And he states that this sort of pragmatism is the tradition of our Fathers. He says this several times, for instance...
"They are not acting rightly who think that our oblation is not pure on account of the names of those who have already died, and who have fallen into heretical tenets, and have not been removed from the sacred tablets; because in fact such matters did not affect the oblation of orthodoxy of the holy fathers also".
Here he is responding to those who think they are more Orthodox than even he is. He says that some of these things don't matter in the long run.
"If we search into this, there is no time at which we shall see the church to be pure. If is already well-known that such things have not and never will cause any injury to the whole fulness of the body of Christ".
This seems to me to show that St Severus absolutely rejected the narrow hyperdoxy which is always a temptation. But there was error and it did matter. Nevertheless this seems to describe the approach of St Severus...
"For I believe that we incur equal danger if we abate anything from strictness in the case of strict and perfect men, and if we show untimely strictness in the case of men who need a dispensation and lawful concession, and give our neighbour, as it is written, turbid dregs to drink".
Of course this requires discretion, and many people prefer a law that can be applied ruthlessly. But this does seem to me to represent the OO policy even in the controversial period. Some people need to be dealt with strictly, others with dispensation, for the sake of the salvation of all.
I note that St Severus states in one of his letters that none of those coming over has been re-ordained, and that those who anywhere dare to re-ordain are anathematised. This in a letter about the reality of the priesthood of the non-Chalcedonians. He is responding to the accusation that people were operating without ordination in the non-Chalcedonians, but he insists both on the reality of the priesthood in the n-C and that the Cs are not re-ordained. This seems to me to quite clearly represent a high view of the sacrament of ordination in the C.
He also states elsewhere that it has been determined that not all those who come from heresies should be baptised, but that indeed those who do so, in the case of Chalcedonians especially, are subject to penalty. This suggests, as we know from the general practice from St Timothy onwards, represents a high and compassionate view of the sacrament of baptism among the Cs.
St Severus does write somewhere to an Imperial official about the requirement that he attends Church services, but I can't find the reference at the moment. Do you remember it?
As far as laity goes, the Fathers are very clear that no obstacles are to be placed in their way. I also think we need to be careful what we mean by Chalcedonianism. Until 553 there had not been that clear exclusion of objectional possibilities which then took place. There are indeed no such things as Chalcedonians, it seems to me. But they are Chalcedonian/Constantinopolitans. This must be taken into account. For myself, when an EO attends Church he has already repudiated any false understanding of Chalcedon by his very presence. Not indeed that I am suggesting he would have held false understandings. And his acceptance of Constantinople 553 seems to me to already have rejected that which St Severus would have required be rejected.
My view is that in the time of St Severus there was no such thing as Chalcedonian laity and non-Chalcedonian laity, as if they were clearly distinguished. I believe that laity made the most of the sacraments they were offered. They could choose the priest to some extent, but not always, and they could not easily choose their bishop. If they were a strict Chalcedonian (and this would not include the vast majority of laity it seems to me) then they would not seek to receive communion from an anti-Chalcedonian priest. And vice-versa. The Fathers seem to have understood that most laity, most rural and working peasantry and tradespeople, were in a different situation to priests, and especially to bishops.
As to the last point. Well I am a disciple of St Severus, but I receive Chalcedon and the Tome in an appropriate manner. We all do. But we are also critical. Things have changed. We do not live in the 5th/6th century, and our Fathers worked towards reconciliation and did not believe there were two Churches, but only one which was disturbed by the teaching of error. We are the disciples of our Fathers living in the 21st century. The EO are not bare Chalcedonians and our later Fathers have also taught that they have the same faith as us. We have never baptised them, or chrismated them, or ordained them, but we believe that they had accepted error.
Shall we look at ourselves? There is error in our own communion. Do we cease to be the Church because of it? We might do. But I believe the Holy Spirit preserves us from such ruin in the end. I believe that he has already corrected that which was objectionable in the 5th/6th centuries.
In that controversial period things were being driven apart. That calls for one response. The creation of schism does demand strictness. But now we are in a different time, where there is the possibility of reconciliation, and where a different response is required. No one living today participated in the events of Chalcedon, or lived in the time before 553. We cannot treat EO as if they are personally responsible, nor we be treated in such a way ourselves. We have manifestly the same faith it seems to me and the Chalcedonian sacraments have never been repeated even in the most difficult of times.