I think we differ in as much that I am arguing against your quest for "fundamentals". For example, it seems valid to argue say that the brain is necessary
for "self awareness", but not that it is sufficient
for self awareness, hence fundamentality is not achieved by that argument. My position is one of anti-reductionism/anti- deterministism and is anti-axiomatic with respect to "existence" itself. As such, I see the "existence of selves" as a sub-issue, not a starting point.
A counter-claim to my position might be illustrated by Heidegger's concept that only Dasein
(being) has Existenz
(existence), in as much that for him the essence of existence is self-contemplation. But we also need to take on board that for him such moments of contemplation/existence are fleeting episodes within the praxis of living. (i.e. "selves" are not evoked most of the time). However we might also note that the later Heidegger (post 1947) turned away from the fundamentality of Dasein
to the fundamentality of language. ("Language speaks the man").
So, I would sum up my position as one which takes relationship/communication to be a priori
to "self" or even "existence". Following Wittgenstein, I would say that the meaning of "existence" in general, and "self existence" in particular is a function of particular contextual two-way interactions between observer and observed. I would merely embellish that idea by pointing to the particular contexts such as those we call "mitigation" in which the phrase "he was not himself that day" depends on such contexts. In short the significance of the word "self" depends on context, not ontology.