Aerodynamics / Aerodynamic Cost / Aero parts

The last tt bike I had I never liked one reason was on the extensions I could jot get to the brakes easily

Just bin the extensions and enter the road bike class where available, or compete on a road bike against people on spaceships for extra cool points

if I had a single speed or fixed gear tt bike I could mount brakes lever on the extensions. Is there anyway I can make sure a crazy contraption work with essentially 4 brake levers.

You could shim some crosstops onto the extensions and it wouldn't interfere with gear levers plugged in to the ends, so SS/fixed is not necessary. You would probably also have so much drag from all the cables flapping around that brakes would be moot 🙂

Is fixed or single speed really quicker

Yes, on the days when you managed to choose a gear which was right all the way round. Most people who have been on fixed for a decade or more can remember that one day.