You do not need to build a static distribution of Qt in order to create programs that can be deployed to PCs without Qt installed. You simply need to deploy whatever shared libraries (DLL on Windoze, .so on linux) and other resources are required to run the program. It is nowhere near as hard as you are trying to make it.

Read the Qt documentation on deployment and pay special attention to the directory structure needed for things like plugins, database drivers, etc. if you use them.