DIY computational fluid dynamics for aerodynamics?
I think you could take this technique pretty far, but probably not all the way (at least usefully).

I see a lot of use for the first part of your plan: taking multiple pictures and reconstructing a 3D model. If you try this for multiple postures I think it should be possible to determine an optimal position for you on your bike based on just looking at the 2D area you take up perpendicular to your riding direction (through the cutout method described in the article about the chung method you linked). 

But this is where the use stops I fear. Some more insight might be gained by looking at the flow of air around your 3D model in something such as the fluid solver you link, but the accuracy is going to be too low to discern between different postures. When you go for that level of detail small things such as the ripples in your shirt or even the fabric of your shirt can have an impact, and the errors you made in the 3D reconstruction will be far larger than the differences you can make by slightly improving your posture on the bike even more than you did in the first step. Apart from this, I think that a fluid solver for movie effects is optimized for visuals first, not for scientific accuracy, so I'd be suspicious of any result it produces.

If you want to try the full fluid mechanics simulation thing you would have to use a 3D scanner or some other very accurate method to produce the 3D models of you on your bike, and then I'd still try and find an actual scientific fluid solver.