Is it possible to get VNC to work like it does on Windows to that you see the main display and not a new clean one?
Um, I think that is a pretty serious security breach, so in general X doesn't allow it. That said, if you are running KDE as your desktop, I do seem to remember there being a program called kdeshare that allowed you to do what you want.
What would be a better solution would be to run the long-term programs from VNC. As long as you don't shut down vncserver, the programs will remain running, even if you close the VNC window. As an alternative, if the long-term programs can dump output to a file, you could follow that with tail
from a VNC window.