i don't think your budget is unrealistic, as long as you're willing to compromise with a few things.
ready-made rigs are usually very expensive (most are overpriced, in my opinion).
i'm a documentary cinematographer - which means i have to be extremely dynamic with my equipment (both video and audio) - and therefore do not use tripod's either.
since everyone has different tastes for equipment, i'm just going to share with you my current set-up as well as the one that is in pre-order in B&H. maybe it can give you a few ideas.
- GH3 (BMPCC in pre-order);
- Voigtlander 25mm f/0.95 (Voigtlander 17.5mm f/0.95 ordered to achieve the same 50mm equiv. field of view and still a good amount of shallow depth of field);
- Panasonic 12-35mm f/2.8 (Sigma 18-35mm f/1.8 in pre-order + Metabones Speed Booster for Nikon F/G Mount, which will give the BMPCC an equiv. 37-72mm field of view and an f/1.3 [and T1.3!] aperture);
- 7 Sandisk Extreme Pro UHS-I 32GB cards (7 Sandisk Extreme Pro UHS-I 64GB cards ordered to cope with the BMPCC ProRes files - I don't plan on using the RAW ability very often);
- 3 Pany GH3 batteries (4 Nikon EN-EL20 batteries to cope with the BMPCC greater hunger for power);
- Rode VideoMic Pro + Rycote Deadcat (way better than the tiny hole on the BMPCC);
- (ViewFactor's Contineo BMPC Cage with the Wood Front Grip - for protecting the BMPCC and having more mounting holes);
- Zacuto Z-Finder Pro 3.0X for 3.2" Screens (this is the only item I'm still unsure will work well - 1st because the BMPCC's screen is 3.5" and 2nd because maybe the mounting plate won't fit the BMPCC too well [and that's partially why I'm getting the cage] - the viewfinder/magnifier makes all the difference though, especially in regards to being able to focus with precision, blocking sunlight, and creating one more point of contact with your body for stabilization purposes);
- Manfrotto 701HDV head + Joby Gorillapod Focus (this is where there's most room for creativity - not saying that this is the ideal rig for everyone, but it certainly suit us pretty well - it's inexpensive, extremely flexible and dynamic, robust and durable, relatively light, and QUITE comfortable when you adjust it properly) - (in case it isn't obvious already, what we do is use two of the Gorillapod's legs for support on each shoulder and the third leg we stretch it parallel to the lens and bend the tip perpendicular to the lens so it serves as a grip - the Focus is pretty sturdy with it's metal parts, won't bend while holding the system, and in conjunction with the viewfinder creates a pretty stable system [as long as you're not going for more than 120mm or so]).
so, this system works quite well for our GH3 setup's and I'm pretty sure it will work even better for the BMPCC. like I said - it isn't ideal for everyone - but if you add all the components up you can get it for a bit more than your budget (in order, all new, estimated prices in USD: 1000 + 1150 + 800 + 450 + 120*7 + 38*4 (+ 35 for an extra charger) + 280 + 140 + 370 + 160 + 100 = 5500.
of course you can go with only one set of lenses (ditch the Voigtlander and your whole cost gost down to 4300), and I'm sure you can find some nice deals of used stuff or you might have some accessories yourself already.
hope this helps!
PS: if you want to add a followfocus, the Viewfactor cage will add, for 150 USD more, a bottom riser block and a couple of 15mm rods, and there are a bunch of ff's in B&H and Ebay for good prices (150 - 400 USD I would say).