There is no "I" in "You"

[Whateverist]

Can anyone answer why you're you.....and not me?

Do you actually assume there would be a reason?

By what method of determination do I experience existence separate from your experience;

The obvious thing to say is that the sensory/cognitive functioning of your organism only feeds into what you call your experience and not into mine.

more to the point, what determined both our particular experiences and could one have been shunt in place of another (by what alternate means could I have experienced existence through your perspective or vice versa)?

This doesn't seem to make sense. Why do you assume there is any 'you' apart from what arises in relation to the experience of your organism?

Why here, why now...why not exist a thousand years from now or a thousand years past?

You can ask this about anything whatsoever. It isn't any more significant asked in this context than in any other.

Can this ever be coherently approached or determined materialistically/scientifically?

No. For science to come into play you would need to ask a coherent question, and one which can then be investigated empirically.

Or, is metaphysics a fundamental necessity?

What do you mean by metaphysics? Is that code for unbridled theorizing devoid of any empirical evidence?

If it is the way experience eludes science which interests you I would think phenomenology is would be the way to go.