I think the status of "late antiquity" changed greatly in the second half of the twentieth century, and with it too, our attitudes towards Koine Greek as a valid period of the language that can be represented and studied in its own right. "Correcting" spellings to conform to the classical norms inadvertently perpetuates orthographic Atticism of Byzantine scholarship.
Even here on B-Greek there is a tension of sorts in discussion between whether reading widely in Greek means going to Classical texts, to one or other of the dialects, to Modern Greek, or to other texts of the Koine period. The ratio of support for each course of action over the short time that I have been involved in this forum would be about 50% for classical, 40% for wider reading in the Koine, and a very little for the other forms of Greek. I believe that all of those periods and approaches are valuable, and have personally engaged with them and introduced texts for reading together on B-Greek, and while the structure of forum was very awkward and frustrating to work within, they are not threads or undertakings that have been ignored by other forum participants. In composition too, there is an emerging realisation that learning to compose using the classical (Attic) idiom, while being of course very beneficial, is not the same as composing in the Koine. While spelling is not going to be a major part of that, the shift from the question, "How would somebody who had just read Plato, Xenophon, or Lysias (or one of the other prose writers that are considered canonical) think of my composition?", to the question, " How would an educated (or not very educated) person in the first or second century CE assess my Greek style and usage, in accordance with Koine norms and nuances?". Reading the language, composing in it and presumably spelling according to the norms it displays is a statement of acceptance and a validation of the value of the language. By the same token, Greek, through a process of historical awareness, is a conservative language, and the Atticism of the spelling was just one example of that process of going back to what was before. The revisionistic movements that have punctuated the history of the language have not been iconoclastic either - they are minor adjustments. The scribes - ranging from redactors to copist, within the proneness of humans to error did what they believed was right or proper to the texts they transmitted. That 8s to say, that I don't think you will be wrong taking either approach, but there are some implications.
The wealth of Koine texts is still yet to be fully explored and/or accepted. They are extensive and diverse, but remain overshadowed by their classical antecedents. By accepting the Classical spelling, you will be stressing the continuity of the Greek language, because as Carlson points out, the Byzantine scribes did indeed align the spelling in later manuscripts to classical norms, and that is what we are used to. By adopting Koine spelling, you will be making a positive statement about the value of the Koine period in the history of the Greek language, and of Late Antiquity as a whole.
Γελᾷ δ' ὁ μωρός, κἄν τι μὴ γέλοιον ᾖ
(Menander, Γνῶμαι μονόστιχοι 108)