Give me a second... little dizzy after spinning around the CP so many times. >.<
Mostly what I'd say is summarized by Youme, but let me expand a bit. What a fly-through does is it showcases a map quickly yet fully. You should focus on what's important (CPs, Important Passageways, Good Detailing, etc.) and then move on. Honestly I never liked the extended-shot method of doing a fly-through unless you had something else to show for it (like watching a kart move in payload).
For this type of film I'd suggest doing a montage instead. That way you can quickly show what needs to be shown and move on. (Also you won't clip through doors, which is one of my biggest pet peeves with level fly-throughs). Also, smaller cuts will be easier to manage then a long extended one, especially if (and hopefully when) you move to the demo smoother (I assume that you're still using gmod).