And, "so what?"  Well, for starters this eliminates infinite regression precisely because any attempt to falsify it would necessarily challenge self-reference itself and evoke self-inconsistency, thereby serving to reinforce the original model.
Personally, I am in favor of indeterminism, since it can 
potentially explain 
why something exists at all. Neither determinism nor your idea of it can explain this 
rationally. Pure determinism gets lost in an infinite recursion, your self-determinism just makes no sense (at least, to me), since it actually evades providing an answer through tautology (logic trickery) while in fact being the same endless (and meaningless) recursion...
In short, I don't particularly care which breed of determinism you stick to
But such a perspective evokes self-contradicition, for if your argument exists as an abstract model, then you must conclude that it, too, is indeterminate, and thus provides absolutely zero determinate value upon anything that you would describe as indeterminate.  You shoot yourself in the foot by precluding any possibility of objectively describing anything.  Your indeterminate model would be mutually exclusive from anything you attempt to squeeze into its scope.  And that's aside from the more simple fact that the word "indeterminism" axiomatically implies you can't use it as a determinate cause for something else.
But, in general you're still missing the point.  A model or theory of something, such as an indeterministic one or any other, is self-apparently an abstract construct.  It is a construct of your mind, as is the nature of 
any theory or model.  You fail to consider any basis by which you can even arrive at such a model, which is unfortunate.  You talk like a Positivist, as if there is some concrete truth of Reality independent of our minds and the models/theories we construct therefrom, and if we only had more knowledge -- of what kind, I don't know, and perhaps you could explain to me 
what, exactly, is the kind of knowledge we would need that would enable us to arrive at some definitive conclusion.  In my previous post, I described the kind of knowledge needed to arrive at such a definitive conclusion.
I am singularly curious whether you understand that your logic (irresistibly leading to conclusions of "zero determinate value" sorts), or any logic known to us for that matter (which we think universally applicable), is also a product of mind, and, as any such product, 
can potentially be falsified (or expanded) from beyond human mind. In other words, it is not given that there is only one, unique logic, or our logic is particularly true (complete). Thereby, it may be you who is shooting himself in the foot...
But it doesn't actually matter here at all, since reality is not an abstract model (a product of mind), so it is in no way tied by our reasoning limitations (which we are obviously not able to grasp, let alone overcome)
Addressing the emboldened passages in order:
1) Is this a possibility?  Simply put, not a relevant one.  Any consideration of this type is totally irrelevant since we are totally limited to our brand of logic.  Accordingly, what 
is relevant is understanding the best that we can do, and I addressed this point by specifically noting that it is necessary to identify the logical limits of our capacity to theorize.  Your consideration, here, can be addressed in similar fashion to how metaphysicists consider hypothetical events occurring outside the scope of perception. "If a tree falls in the forest and it is not observed, did it actually fall?"  Bad question, as we totally lack any means of providing a definitive answer.
2)  This statement negates itself.  When you say, "Reality is not an abstract model," that in itself is an abstract model.  Even simply saying  'Reality exists' is an abstract model.
A theory/model is simply a description of something.  That's it.  For example, if you open a dictionary, every single definition is an abstract theory of the thing described. This is inescapable. You cannot talk about Reality's existence outside of the abstract models we describe.  Phrased another way, no model/theory of Reality means that we can't even affirm Reality exists.  The existence of Reality is totally dependent upon a theory of it; no theory --> no Reality (that we can affirm or is of any relevance to us).
Edit:  When I say that theories/models are simply a description of something, I would clarify this by further noting that it is precisely due to theories/models that Reality and its constituents are 
defined.  In the lack of a theory/model, there is no definition -- literally.  Reality gains its definition in a literal sense via theories/models, and the mechanism by which this occurs is a metrical one.  That is, theories/models employ metrics, i.e. abstract scales of measurement, to define Reality.  This starts getting into the reasons why I believe in Intelligent Design, for without a mind to employ metrics with which to define Reality, Reality entirely lacks any definition, including the fundamental definition of "existence."  "Existence" is born of a simple difference metric, i.e. "1 vs. 0," or "yes, existence vs. no, not-existence."
Edit 2:  To exemplify my first edit, consider space.  If a metric is employed which can be divided infinitesimally, then space is continuous.  If instead a metric is employed which cannot be divided infinitesimally, then space is discontinuous.  Neat, eh?