Honestly, seeing the high-level requirements for what constructor theory defines as Possible / Impossible, I mostly expect that it will have to conclude that many of the transformations that happen in QM are Impossible (a constructor can't be conceived that could achieve those tasks with arbitrary precision and reliability).

Related to your observations, I believe you are absolutely right in that it's likely we've sort of reached the end of the road in exploring beyond the quantum scale with the current approach. I do believe there are some dangling threads that can be pulled to help guide some other directions - such as the measurement problem and the no-communication theorem.

I also have some hope that computer theory may be able to shed some light - at the moment, we have a clear distinction between quantum algorithms and classical algorithms, but we don't know if they are fundamentally different or not. A discovery of how to efficiently compute quantum algorithms on classical computers (i.e. BQP = P or at least BQP = NP) would likely be a major insight into QM itself. Conversely, proof that quantum computers are fundamentally different from classical computers would also hopefully show WHY/HOW they are different and help in this area. Alternatively, if it turns out that quantum computers are in fact not physically realizable or require exponential memory or energy would essentially prove that physical reality does not obey some of the properties that make quantum computers (apparently) more powerful than classical computers.