Sorry, perhaps I just don't know what "monism" truly means, I admit my ignorance, but if we just limit ourselves to the mind-body problem, I just meant that a dualist position considers the mind as separate from the body, and monism rejects that.

The functionalist point of view you propose doesn't seem to be to be useful at all in this context. Let's backtrack. The original example I provided you when you asked about whether there can be somebody proposing monism and at the same time holding dualist positions was asking:

"If I do mind uploading, do I die?"

You can be creative in redefining what the word "I" means, which is what you engaged with, but when push comes to shove and I do the actual mind uploading, then the self that experienced my qualia since birth will irreparably stop experiencing qualia (aka: dying) and be replaced by another self. You're free to call that self as if it was me, and be all happy it can do the same things I could do, but that's not gonna change the fact that my previous self (the only "I" that matters to me) died.

Would you step in the Star Trek teleporter knowing that you will die, and think you haven't died just because you have been replaced by a different being that is functionally equivalent to you? I sure as hell will never do it.