Well, couldn't you technically do it through FRED. Just have a SEXP that changes your model so that when you're in the cockpit, that is the model being used for your ship, but when you switch to another view (exterior, looking at another ship... whatever) your model changes to the fighter model. Then when you switch back into cockpit view, a SEXP changes your model back to the cockpit model.
Also, couldn't you make a blank texture for the monitors inside the cockpit, and then alter the hud itself, so it *appears* to be displayed on the monitors. If we want it to look real good, we can make a fake hud texture for the monitor. That way, it will still look like the hud is being displayed on the monitors when the player uses free look to look around the cockpit and the hud disappears.