In some books by the Gallery of Magick there’s this arrangement of archangels you mention (Raphael in the South, Michael in the East).
They give an explanation of why they have chosen this way of doing the call in the book “Archangels of Magick” by Damon Brand, but in a few words it was a matter of personal gnosis validated by ancient sources research.
I don’t think the GD purposefully deceived people, nor that their chosen arrangement was necessarily wrong. Things change, but in the end, directions are just one of the many things that are part of a ritual. Even if you get that slightly wrong (which still has power of its own, being used by thousands of occultists throughout the centuries), but the intention is there and the other parts are correct, rituals can still work.
For example, we don’t have the correct pronunciation of all the words of power we often use in rituals, or some Demons/Angels sigils you find in books have been altered, or we don’t necessarily work under the right planetary influences or time/day, etc.
Rituals still work. Some more, some less. I guess that the more things you get right about the process, the better the chances you have for it to work.
I would suggest you to try both versions and see which works best for you.