So who does the task of tackling these hard questions fall to? Scientists who dabble in philosophy and aren't afraid to publish unscientific theories? Philosophers who dabble in physics or read popularized versions of experimental results and interpretations of QM? Or has the academic community overall decided to give up on substance metaphysics?
An important fact to consider before answering the question are the goals of science and philosophy (which includes metaphysics).
Science seeks for empirical truth. Thermodynamic laws can be verified to a reasonable value of certainty just with simple tools as a thermometer, from a scientific standpoint. Now, consider this: temperature is a feeling, a simple metaphysical fact, which in physical (scientific) terms is quite difficult to approach. But that's not a problem of science. Science solves the issue just by adding an additional law (which, sorry, should have been there from the start, so, let's call it zeroth law!) saying that thermal equilibrium between systems is a transitive relation. Now, what the hell is that? You want to be precise and dig into that? Impossible. Any dictionary (even technical ones) is just a circular set of crossed-references. But that's not a problem of science. Science seeks empirical truth, not final truths.
The discipline that seeks for deeper truths is philosophy. Philosophically, yes, there are issues in thermodynamics, but not only there or in QM. There are far more deep problems. For example, just to start, the central axis of rationality: induction, which C.D. Broad said to be "the glory of science but the scandal of philosophy". QM, in such regard, is just a minor issue. How can QM be important, when reason itself has a broken gear?
To your punctual observation: let's say that science focus mostly on the object (see scientific realism and metaphysical positivism), and not on the subject. The subject would be essentially a metaphysical problem. QM proved impossible to assess only from the perspective of the object, without considering the subject.
So, by asking "who should work on QM?" it is already assumed that this is an issue demanding specialists (for example, either the philosophical or either the scientific community), and NOT generalists, which is a fallacy. In order to work on any issue, all the necessary background must be applied, that is, scientists and philosophers.
And here a problem raises: while philosophers are, since s.XVII, concerned with the issues of science and philosophy, and trying to enter into the scientific debate with a large disadvantage, scientists have taken a path of apparent independence of philosophy. Consider Richard Feynman saying that "philosophy of science is as useful to scientists as ornithology is to birds"... while he himself was one of the most remarkable philosophers of QM. Such is a quite important issue that needs an urgent solution. But no solution appears in the horizon for now. And the problem is moreover growing:
The distance between philosophy and science is not decreasing but getting larger with time. From my personal perspective, the fallacy is mostly on the scientific side: scientists believing that pure science, independent of the subject and its metaphysical issues, is possible. Scientists believing that science without foundations, without goals, without essence is possible. Making science nowadays is just publishing observations performed using the scientific method (which extent and application domain, in addition, are largely debatable).
On the other hand, philosophers have not supplied the necessary knowledge to produce scientific knowledge that would embed the elementary metaphysical principles. Immanuel Kant prepared the background to such goal: the formalization of metaphysics. Kant (successfully, IMHO) proved that metaphysics can reach the level of a science (which I interpret as getting a sufficient systematized formal background, as in any scientific field). But it seems that such task never got any follow-up. From a personal standpoint, I precisely work on a book about such subject. But the task is huge, it is not of academic interest, and it even sounds strange: who would want to formalize metaphysics, all that stuff about God? (such is the current understanding of metaphysics... and it is radically wrong: clearly, metaphysics has a bad reputation, mainly between men of science).