Basically the answer lies in re-mapping the keyboard. Remember the VNC Client is reading your keypress and x11vnc is interpreting that on the NIT. Just like with Bluetooth keyboards, you can re-map keys to specific functions and load that Map via Xmodmap (easiest for me) when opening the VNC CLient on the far end (ie open terminal run Xmodmap - haven't found easier solution on NITs yet)

Then when you hit say Shift-F6 you can have x11vnc interpret that as Fullscreen switch.

Don't ask me how to re-map all the keys as I haven't spent time figuring out all the mappings, but I know it can be done as I have done it in the past with other machines.