However, I still worry about this issue.
Worry in what sense?
Well, you wrote:
At the same time, because we know it is possible to receive individuals who have the 'form of baptism' (a term which comes up in St. Basil's letter) but not (per the last point) the One Baptism of the Church, and we know that everyone *must* be baptized, then that leads to the conclusion I gave--that the One Baptism exists only within the Church, but the Grace of that baptism can be conveyed, at a later date through the vehicle of the 'subsequent' Mysteries (i.e., those that normally come after baptism--Chrismation, Confession, Communion) because the One who provides the Grace of Baptism is the same One who provides the Grace in the subsequent Mysteries.
If that were true (I'm not saying it isn't), wouldn't that mean that, say, receiving the Precious Gifts from week to week conveys sufficient grace on the recipient so as to exclude the necessity of baptism, chrismation and confession entirely? The logic you are presenting seems to imply that grace is grace is grace is grace, if you know what I mean?
Actually, we have an epistle from St. Dionysius the Great
(a contemporary and ally of St. Cyprian's) on that very subject:
For one of the brethren that assemble, who has long been considered a believer, and who, before my ordination, and I think before the appointment of the blessed Heraclas, was a member of the congregation, was present with those who were recently baptized. And when he heard the questions and answers, he came to me weeping, and bewailing himself; and falling at my feet he acknowledged and protested that the baptism with which he had been baptized among the heretics was not of this character, nor in any respect like this, because it was full of impiety and blasphemy. And he said that his soul was now pierced with sorrow, and that he had not confidence to lift his eyes to God, because he had set out from those impious words and deeds. And on this account he besought that he might receive this most perfect purification, and reception and grace. But I did not dare to do this; and said that his long communion was sufficient for this. For I should not dare to renew from the beginning one who had heard the giving of thanks and joined in repeating the Amen; who had stood by the table and had stretched forth his hands to receive the blessed food; and who had received it, and partaken for a long while of the body and blood of our Lord Jesus Christ. But I exhorted him to be of good courage, and to approach the partaking of the saints with firm faith and good hope.