I saw this Project too.
BMCC also does what they want already at similar price and EF lenses

You can use the 1100D, most of the stuff is similar... but you get a smaller LCD and no crop mode and no audio input. Plus you'll have to do more DE-crippling in the firmware.
Probably all of these cameras will work to some extent, the sensors aren't really the problem. Noise is passable up to iso 1250. I get better performance on 600D than 400D in terms of that so I think smaller/larger sensor won't make a difference. Just limited by memory size, write speed and canon software.
What makes a cinema camera? At least 4:2:2 color, not so compressed video and somewhere around 2k resolution. Also good audio support. We're like 1/2 way there. The 30 min limit seems hard coded somewhere but most takes are way under that.
mirror and the shutter
Mirror already goes up and shutter stays open.
Unless you're really into doing the HW part, I'd look at the software and try to fix it. You'll have to do it anyway for the mods and then some.