Thanks again for your great essay, and your appreciation of mine. In response to your statement (on my own thread), that "arguments can't decisively show what to think about determinism versus true indeterminism", I can offer some general, if somewhat dogmatic, arguments about causality. (This is posted on my thread as well).
Following Hume, there is no causation in Nature. The appearance of it results from confusing cause with logical implication. This is a 'category mistake', like mixing mental with physical domains. The only truly deterministic systems are deductive systems, for the only 'necessity' is logical necessity. This is always a matter of definition rather than of fact, so that the "mistake" is confusing 'the found' and 'the made'.
Similarly, randomness pertains only to mathematics, not to physical reality. Whether Nature is random is not a decidable question. The IDEA we have, of random physical processes--lacking, as you say, logically bound outcomes--simply reflects this confusion of the found with the made. We are never in a position to establish logical necessity (cause) in Nature (the found), and only sometimes in mathematics (the made). In other words, 'random' is a mathematical concept, not a physical one. Randomness in Nature, like causality, can only be a metaphysical assertion--that is, independent of decidable physical fact. (Historically, it was religious, since all cause was ultimately traceable to the First Cause.) If so, then experiment would be irrelevant.
We cannot make meaningful ONTOLOGICAL assertions about events in Nature being either determined (caused) or undetermined (random). But we can make assertions about our own state of knowledge; we can say that something is 'undetermined' in the sense that for us it is undecided or unknown. This is not an assertion about Nature (the found) but about science (the made).
The term 'determinism' is traditionally ambiguous. It can refer, on the one hand, to what can be determined epistemologically; on the other, it can refer to an ontologically real relationship of causal power existing between things or events. I believe there can be no determinism in this latter sense--and therefore no 'true indeterminism' either. The only determinism is logical implication (provability), and the only deterministic systems are deductive systems. The only indeterminism is logical undecidability.
I do make statements in my essay to the effect that the apparent randomness of Nature supports its "immanent reality". I do not mean by that, however, to say that Nature is intrinsically random. It is rather the state of our own uncertainty (not Nature's) that requires us to regard Nature as bearing its own full reality--precisely because it cannot be fully accounted for in some deductive system. It is real because it is not a product of our definitions, because WE cannot determine what it is. This is separate from the question of whether it is 'determined' (causally) within itself, which is not a question we can answer. We imagine that it might be so determined, but what we are really thinking of is the logical determination within our own thought systems.
Hope this is useful.