@Shauli
If part of a conceptually infinite being (אין סוף) [as opposed to an indefinite infinity] was ‘separated’ from the rest, that which was separated will contain in it all that it had originally. Thus a ‘part’ (חלק) can be no different than from where it originated from.
Therefore all your points would seem irrelevant, since all you are proving is just that it is ‘part’ not the ‘full’ thing; but you admit to it being ‘part’ of אלוקות ממש, (unlike your original objection).
As to the Avos, see the Shefa Tal there where he draws a parallel between every Jew. But furthermore we are talking about Tzaddikim.