No need to move core things manually. After setting the core dir correctly and moving only the project directory to a space without paths, reopen the project at the new location and build again. It should install PlatformIO in the designated path.
Another workaround is to create an empty .platformio folder in the root of the main drive (usually C:, => C:/.platformio). PlatformIO installer will automatically pick that folder and use it later for all operations.