We use the sigma 18-35 w/ speedbooster and it is big. Amazing lens, and really improves the camera in lowlight, but it makes the camera about the same size and weight as our 6d and 24-105. No real experience, but I looked at the rokinon 12mm 2.0 for some travel stuff and it seems pretty small. Also an old Pentax 50 1.4 w/ canon adapter on the speedbooster is a pretty great portrait/shallow look combo in a small package. 12-35 seems to be the best bet for running around if you need a zoom to be able to react.
If all you need is XLR in, grab one of the tascam recorders that screw into the bottom of the camera like the Tascam DR-60mkII. We use that with a GH4 and it works great. It is kind of a bulky unit together, so we mainly use it like that on a tripod in production type settings. For running around, we usually keep the tascam separate and sync later.
Don't forget about battery life either. The total kit weight is what's really important if you're hiking all your gear in. BMPCC might be lighter than a GH4, but with the not ideal power consumption, the total kit for the same amount of shooting time might be heavier than GH4 which has pretty good battery life.
Dave, I looked at your examples and have a few general comments. The best looking shot on your video was when you got focus while closeup on the pay phone keys. I paused on these stills and it is more than sharp enough! I do not think camera or lens is your limiting factor.
Your test video to me was very shaky, try a tripod and carefully composed locked off (stationary, non-moving) shots for your next tests and see if that helps. Your grading is also very very contrasty compared to the other two. Your blacks are very crushed and the color pretty saturated. The other videos you posted show the more popular "raised black" look with more de-saturated colors. This doesn't make their videos sharper, but does reveal more details in the shadows.
All of the videos you shared have a significant amount of aliasing. Somewhere in the process of ML raw to vimeo, aliasing is pretty apparent on most fine detail. This is made worse on shaky shots. Based on this and using around with ML Raw on my eos-m, I would recommend against using it for anything other than tests and playing around with a raw workflow (unless you have a 5d). The civic video obviously looks the best but most of the improvements are due to lighting (shooting earlier in the morning or later in the day) and smooth camera motion and not so much based on the RAW workflow.
If I were you, I would get a tripod, go back to shooting full 1080 HD on the t2i, use the neutral picture profile with sharpness and contrast and saturation turned down (search prolost flat online) and try shooting scenes with less dynamic range (more even lighting). Then, once you have gotten some good stuff, I would look at fast aperture primes lenses and then maybe a camera upgrade to something like a gh4 with a metabones adapter. But based on your example, you still have a lot of room to develop with your current setup. Have fun and don't feel limited by gear!
I agree with Guy, t2i is perfectly capable of making good images. You say you are after "crispness" which got people talking about solving sharpness (which is not the t2i's strong suit, but it's not abysmal). I'm not sure that's enough for us to go on. Please post examples of your footage vs. a link to something you are trying to emulate but can't achieve.
If the only lens you have is the kit lens, I would advise you try out a nifty fifty or something with a wider aperture to see if what you are really looking for is the increase in perceived detail when you isolate a subject from the background using wide apertures.
I think it is the wrong path to chase a look with technology (ML raw, plugins, new cameras) unless you know precisely what your current setup is lacking and how your new solution will fix it. Exposing correctly, creative composition and minimizing camera shake (use a tripod or cheap monopod) should get you 80%+ of the way to good looking footage, even with a t2i.
We own the GH4 and 6D and I think they make a pretty good team. If I could only choose one, I would choose GH4 in a heartbeat. We mainly do doc, sports and weddings and the gh4 is just more video focused for those applications. The image is sharper, no record limit, real audio monitoring (combine it with a tascam audio recorder for a cheap solution for any interviews), 4k allows for nice punch-ins for small interview setups, better slo-mo. We too have all EF glass, but the metabones is fantastic. Metabones + sigma 18-35 allows us to shoot in all but pitch black and still get acceptable noise for web based doc work. Sell one of your less used EF lenses and use it to buy the metabones.
6D is nice and we will probably end up keeping it around just for stills even if we upgrade to something like an a7s later. We use it with an 85 for nice shallow portrait FF looks and with a 14mm for super wide establishing shots (watch your moire, sometimes we just have to deal with it). Moire is the biggest annoyance with this camera.
As another poster said, If you go with the GH4, you can shoot regular HD instead of 4k. Our computer isn't great so we adopted a proxy workflow for editing. It works but the trade-off is added hassle and time spent re-linking. I plan on using this footage for reviews/reels later so I'd like to capture at the best quality but it has been a lot of work for probably a little gain down the road.