T2i 1080p video sucks. Or I'm doing something wrong.

[Cattykit]

http://www.youtube.com/watch?v=kgQE_celpt8

Check out @ 2:25

On another note, the D800 resolves a tab more detail than the 5DMK3 but it has absolutely atrocious noise at higher ISOs.

D800 does resolve more detail but it's still filled with line-skipping problems. Considering your line of work, those are things you really need to avoid.
Though 5Dmk3 is softer, its line-skipping problems free and you can easily apply basic sharpening to deal with its softness.

https://vimeo.com/39292404

 

[Cattykit]

BTW, if you're concerned about DR, you might want to do more research on GH2: It's the weak spot of the camera.