There's simply no room for discussing this with dogmatists like yourself. Your dislike of Rings of Power means you will dismiss out of hand anything anybody says, even when they're discussing something that comes "straight from the source", if you will:

Olórin (who was known in Middle-earth as Mithrandir) brought it with him out of the West. And on a time Olórin came to Galadriel, who dwelt now under the trees of Greenwood the Great….. And when Olórin had told her many tidings she sighed, and said: ‘I grieve in Middle-earth, for leaves fall and flowers fade; and my heart yearns, ing trees and grass that do not die. I would have these in my home.’ Then Olórin said: ‘Would you then have the Elessar?’ ….And he held before her the Elessar, and she looked on it and wondered. And Olórin said: ‘This I bring to you from Yavanna. Use it as you may, and for a while you shall make the land of your dwelling the fairest place in Middle-earth….

And when did Galadriel and her followers found Lothlorien? That's right. The second age. Extrapolating his presence in Middle Earth in the second age from this age is not difficult.

"It also states that it is unlikely that Gandalf ever journeyed any further east than Harad"

And? Rhun (where Gandalf is in the show) is in Mordor, which is furthest west than Harad. Honestly. You just want to pooh pooh on anybody defending this show, don't you?

Except in Unfinished Tales (that's Canon right?) Tolkien talked about Olorin spending time in the East of Middle Earth during the second age. Was this as Gandalf or as himself, the maia? We don't know because he sadly ed away before finishing that part... so there is plenty of room for interpretation there.