My problem with CDB using MSVC is solved.
Turns out it's a pretty common problem, not at all related to Qt. It's caused by the existence of pre-existing Visual C++ redistributables. The installation works perfectly (in my case) after they are uninstalled.
There are loads of pages that describe the many causes and solutions, but this one seems to be the clearest:
http://notepad.patheticcockroach.com/1666/installing-visual-c-2010-and-windows-sdk-for-windows-7-offline-installer-and-installation-troubleshooting/
Hope this helps others who may be suffering from the same problem.