>on Windows, you need to copy a dozen .dll files until your executable launches
Presumably you're new to Windows development? as long as you place the libraries in the same folder as the executable, add the QT install directory to your path, or add the install direvtoey to your debigging Environment variable, you're laughing - it's as straightforward as DLLs on Windows come.
AFAIK, static linking doesn't necessary make the whole project LGPL. You just need to provide users relink LGPL part of the library.
The problem is that I don't know which libraries I need. For a very small project I just kept launching the .exe and reading error messages until I had gathered all the DLLs. It's not a sound way to do it, in case a library is loaded dynamically.
This, and there are also applications which state which DLLs are missing from a deployment.