Is the phrase "for one of both of us" grammatically correct?

In portal, Glados at one point says this: “and I thought of a solution that would be the best for one of both of us.”

I am debating about whether or not the construction of “for one of both of us” is grammatically correct.

My first opinion is that this is incorrect. Following the words “for one of”, you can either:
* list two alternatives (e.g. “…for one of X or Y”)
* or you can list a single noun that represents a collective (e.g. “…for one of the group”).
You cannot treat “both of us” as a list of two alternatives because ‘both of’ explicitly means they are not alternatives. If you treat “both of us” as the name of a group, then you would have to pre-pend it with a particle. This makes “…for one of the both of us” to be more grammatically correct, but still exceedingly awkward. Consider “…for one of the three of us” vs. “for one of three of us”.

Anyway can someone clear this up?

If my above opinion is correct, can someone explain it in clearer grammatically terms (i.e. preferably with grammatical concepts that I can verify on say, wikipedia or an English textbook).

If I am wrong, can someone explain what is flawed about my above opinion? Is “both of us” in Glados’ quote considered a collective noun? If not, what part of speech is “both of us” in that sentence?