Companionship in Frankenstein

I've been re-reading Frankenstein lately, and I've been noticing a lot of comparisons that the creature makes between himself and Adam & Eve and - by extension - the Garden of Eden.  (I feel like I should note that I don't want to use appellations like "the creature" or "the monster," but that character never gets a proper name, so....)

The creature wants a companion.  In Chapter 20, he rhetorically asks, "Shall each man find a wife for his bosom, and each beast have his mate, and I be alone?"  The creature casts himself as Adam in Genesis or - more appropriately - Milton's Paradise Lost, which, in earlier chapters, he mentions that he's read.

But what's more interesting than just the creature's wanting a companion with whom he can live is how that wish parallels Victor Frankenstein's wish.  At the beginning of Chapter 17, the creature explains to Frankenstein that if he consents to make him a companion, "neither you nor any other human being shall ever see us again; I will go to the vast wilds of South America."  He also says, "It is true, we shall be monsters, cut off from all the world; but on that account we shall be more attached to one another.  Our lives will not be happy, but they will be harmless and free from the misery I now feel."  The creature sees having a companion as a sort of escape from the miserable situation that he is now in, and Victor Frankenstein views his impending marriage to Elizabeth in the same way.  In Chapter 18, he narrates, "For myself, there was one reward I promised myself from my detested toils - one consolation for my unparalleled sufferings; it was the prospect of that day when, enfranchised from my miserable slavery, I might claim Elizabeth and forget the past in my union with her."  Both Frankenstein and his creature seek a solace from their misery (both use inflections of the word) in companionship.  Both of these are akin, if not exactly parallel, to Adam's companionship with Eve.

What I'm still a bit confused by is the creature's self-imposed exile.  I can understand it as it is, but if the creature's meeting a companion is reminiscent of Adam's meeting Eve, then the creature's exile is similar to their banishment from the Garden of Eden.  If the Garden of Eden is a paradise, it doesn't make sense for the creature willingly to "quit the neighbourhood of man," as Frankenstein calls it in Chapter 20.  Maybe I'm just extending the similarities too far.

Frankenstein never actually makes the companion for his creature, so maybe it doesn't matter that the Adam & Eve/Garden of Eden parallels don't quite match up, but it is really interesting how Shelley mixes up some of the elements in Genesis and Paradise Lost.