I've thought quite a bit about the distinction between the different sub-disciplines, but this post and the linked one have revealed to me that I don't usually make a distinction between theoretical and quantum chemistry since I'm biased by doing almost entirely electronic structure. I almost never use "quantum chemistry" but "theoretical chemistry", and don't really distinguish between them, which is wrong, because I think theoretical chemistry encompasses areas beyond just quantum chemistry. I've included links to the respective Wikipedia articles, though this might just add to the overall confusion.
Theoretical chemistry deals with the physical foundations of chemistry through mathematical models, both exact and approximate. This includes quantum chemistry and electronic structure theory, kinetics, molecular biophysics, theoretical spectroscopy, "atomistic" models for bulk materials, and many other sub-disciplines I'm sure to be missing. I'm lumping both the creation of the mathematical models and their implementation together under this banner, though traditionally the focus is more on the former than the latter. The latter may still be ill-defined...
Quantum chemistry is the use of quantum mechanics within chemistry, technically both experimentally and theoretically. I tend to think of this as nothing more than a synonym for electronic structure theory, but this is also incorrect. Probably most of modern theoretical chemistry falls here, and even classical models can be derived as limiting cases for quantum ones, though I wouldn't place the most common instances of molecular dynamics here.
Computational chemistry is the application of computational programs to chemistry, where those programs are the implementation(s) of ideas from theoretical chemistry. It is solely the use of tools to solve chemical problems, not the development of those tools. These applications don't have to be quantum mechanical in nature, either.
You've already touched upon this:
Still there are some types of questions which are almost exclusively about real-world computations and have very little to do with the theory, such as, for instance, the questions on which keyword can one use to battle the SCF convergence issues in some program and the like.
Opinions on tags (with examples)
The quantum and computational chemistry tags
From my short experience on Chem.SE, I am in agreement with everything in your post. I don't think quantum-chemistry should necessarily be within the scope of computational-chemistry, and vice-versa, but this is also just a restatement.
The distinction between quantum-chemistry and computational-chemistry is the most clear one in my mind, or perhaps here is where my bias really shows.
Here are good examples of tagging. I'm not considering whether or not theoretical-chemistry (or any other tag) is appropriate here.
Here are some not-so-good ones.
It may appear that I'm just trying to retag everything, but specific examples help form the correct duck test.
The theoretical chemistry tag
By the logic above, the theoretical-chemistry tag has the danger to be misused more easily than the others, since it is the broadest in scope. It might be easier to identify posts that don't fall under this tag. Perhaps bringing up specific examples will help us better define theoretical-chemistry.
Here are examples of questions I feel should not have the theoretical-chemistry tag.
Other than the above mis-tagged questions, I've seen few discussions about theoretical-chemistry that would fall outside the scope of either quantum-chemistry or computational-chemistry. Here are some that I feel are good examples for not falling cleanly either either quantum-chemistry or computational-chemistry, but are theoretical in nature.
Now for some that we could debate about, for a multitude of reasons.
Again, these are just my opinions. I think I know what theoretical chemistry is, but I don't know what the duck test for theoretical chemistry is in the context of Chem.SE.