Dear Paolo,
I see some similarities of your ideas with mine (see my essay A Mind/Mathematics Dualistic Foundation of Physical Reality): you wrote "The obvious answer is that existence is a quality relationally attributed to entities by Sentient Agents", and it pertains only to their current status or informational content. We are forced to say that something exists if an only if a SA is aware of it. The quality of existence comes out to be, firstly, deeply relational, and secondly, inseparably related to the awareness and knowledge one has about entities".
In my view, there are 2 different concepts of existence that need to be distinguished: one is the mathematical existence, which is a purely abstract, mathematical concept independent of all contingencies (independent of the whole physical universe). The other is this contingent form of existence that you mention, that is for an object (be it mathematical or not) to be either created or pointed out (distinguished) here and now by conscious perception. I have explained in my essay how the laws of quantum physics can be explained from an interplay between these 2 forms of existence.
You talk about "Nominalist approaches" that "deny an independent ontology to the mathematical objects". I think, the main reason why philosophers of mathematics keep talking about nominalism, is that they failed to update their discourse to the consequences of the Completeness theorem. Indeed, this theorem shows that the existence of the objects of any consitent theory can be directly produced by its formalism itself as soon as we admit an actually infinite set of natural numbers. In these conditions (and just if we admit the existence of an infinity of natural numbers), there is no fundamental difference of nature between the objects of a theory and its formalism, and there is no sense trying to oppose them. We need not wonder if we allow or deny an independent ontology of mathematical objects if the objects do not need any independent ontogy, since the formalism is already sufficient to provide the ontology that is needed. With the only defect, of course, that building the whole system of objects requires to consider the whole infinite set of all possible expressions of a kind that can be written from the theory, while sentient agents can only explore a finite set of expressions at each time.
You asked the question of "how mathematical entities could 'exist', and having causal impact on reality, without being physical. A possible way out could be forcing their stance of 'being real', equating the physical reality to a mathematical structure.". Indeed, a possible way for 2 things to be related is to consider them identical, but there is quite a margin of possibilities in details. In particular, in the idea of "physical reality" I distinguish between the things that are real, and their quality of being real. So, I see the things that are "physically real" as particular cases of mathematical structures, while I attribute their quality of being physically real, to conscious perception.
However I would diverge on the following: you wrote about "...phenomena potentially not addressable in mathematical terms. In fact, rephrasing it as 'if there could ever exist aspects of reality non describable abstractly', and sticking to the conscious, relational meaning of existence, we may conclude that it cannot be the case". Maybe your use of the word "abstract" is ambiguous : while I would agree that things have to be consciously perceived for being "real" (beyond a mere mathematical existence), I think that "being perceived" does not imply being mathematical, as we are also able to perceive some non-mathematical stuff (feelings, etc: not everything we can understand is a mathematical structure, especially for people who are not mathematicians).
You may also be interested to see my review of essays, with a list of those I found most interesting (unfortunately I'm still far from finishing to read all I wish... the link to your essay will appear in the next update).