Ok finally got the depencies right on my machine to do the build successfully. After running the built binary, it seems to display the graphics fine, without having to use the dedicated graphics card.
Copy/Paste still isn't working, but I'm happy at least that the graphics seem to work properly now.
I do suspect this means there is something in the AppImage build process that my machine doesn't like. Finding out what that is might be the next step I suppose!