Yes, there are many things that go into making filmic-looking images such as location, lighting, etc. and of course the story is important, but OP is not asking about that, he is asking about what camera he should buy. Camera choice is very important because it can change your entire workflow. I can see why you want a camera that is good in low light, as you're doing a lot of work in natural light.
The A6300 was a really promising camera on paper, but the overheating issues and awful rolling shutter make it pretty unusable in my eyes. The video quality in HD might be marginally better than on the 7D (don't quote me on that though) but you will see significant improvement in Low Light and Dynamic Range. The other advantage of shooting HD is I think it won't overheat (not 100% sure about this though) and rolling shutter will be way better.
The GH4 is worth looking into (even if it's pushing your prince limit slightly) because it is jam packed with great features. While it's low light performance is about the same if not a tiny bit worse than the 7D (usable up to ISO3200, 6400 is ok but you'll definitely have some ugly noise), it's dynamic range is slightly better. It also allows you to shoot 4K which is a really nice bonus. You can get a used one for about $1,100 (US) on ebay.
Another huge advantage of this camera is that it outputs a 10-bit signal through HDMI which means if you have an external recorder you can record much higher quality video. I definitely think this camera is the most versatile on the market right now (for its price) and it will definitely give you all the tools you need to make better quality content.
The G7 is way cheaper than the GH4 but has less video features (you'll have to look up what you'd lose), but just the fact that it costs half the price of the GH4 is pretty impressive. Its dynamic range is worse and the GH4 as it doesn't have V-Log or CineD, but its low light performance is slightly better. In 4K the video quality is pretty damn close if not a hair better than the GH4 (due to less noise) but in all other video modes, and especially in slow motion, the video quality becomes pretty mediocre.
I would also highly recommend looking at the blackmagic pocket cinema camera because while it's only HD it can give you the most filmic image of any camera in its price range. It definitely has it's quirks though, so it would be worth researching. You get one new for $1,000 and used for way less ($600 range). It's worth mentioning that it's lowlight performance is pretty bad, and I wouldn't recommend going above ISO1600. It also only shoots up to 30fps, which I realize isn't great for you. Blackmagic also just released the micro cinema camera, which is pretty much exactly the same performance-wise but it can do 60fps. The downsides of this camera are that it comes without a viewfinder ($200 to buy a cheap one) and because it only just hit the market, you won't be able to get one used (it costs $1,000).
Now you mentioned that you'd want to still be able to use your canon lenses on whatever camera you buy. Both the GH4 (and G7) and the Blackmagic are micro 4/3 mount, and they both have similar sensor sizes which are around 16mm this means that you will get a 2X crop on all lenses (slightly more on the BMPCC, I think) which means that a 50mm lens suddenly has the equivalent focal length of a 100mm lens. This isn't that far from the 1.5X crop of an APSC sensor (what the 7D has), but it can make a big difference if you're adapting lenses (native Micro 4/3 lenses compensate for this crop by being extremely wide)
The solution to this is to buy a speedbooster. The best one you can get is made by Metabones, but it will cost you $650. You might be able to snag a used one for $400 if you're lucky. There are cheaper third party options, but Metabones really is the best and most reliable one out there (it will still give you electronic control of your lenses, but it will make autofocus a lot slower) A speedbooster not only adapts your lens from M4/3 to EF but also reduces the crop factor of small sensors from 2X to about 1.6X which is basically the same as you've been using. It also makes all of your lenses the equivalent of one f-stop faster. This means that a f2.8 lens becomes an f2 lens. This extra stop really makes a huge difference
Anyways, I encourage you to look into each of these cameras on your own, and I hope this was helpful. Best of luck and keep on making good content!