Jason, FYI:
The D5300 doesn't have a headphone jack.
Any claim that the GH3 gives better video quality than the D5300 is entirely subjective. The GH3 has better resolution, but the D5300 has better dynamic range, colour, low light and a larger sensor. I prefer the D5300 image to the GH3's. The GH3 is easier to use for video, so in that way you may get better video from it. The D5300 is a bit of a pain to use, but if you're talking about graduating to pro stuff like BMPC4K down the road, you need to learn your way around a camera anyway.
The G6, GM1 and GX7 are the only Panasonic models with focus peaking AFAIK.
Personally I wouldn't buy any Canon APS-C DSLR - including the 70D. Moire, aliasing and softness are deal breakers for me (and relative to D5300 poor low light and DR too). I own a G6 and a D5300, having sold my Canon 600D because I was tired of softness, moire and aliasing. You'll get that with a 70D too. Autofocus might be nice, but if you're looking to learn how to shoot like a pro then manual is the way to go.
The G6 is by far the best deal out there at the moment for video. I would recommend it as a perfect camera for a beginner who wants to learn how to shoot video 'properly' - it has all the tools you need and is so easy to use compared to Canon, Nikon etc. The difficulty is deciding whether to go for MFT glass or get an adapter/speed booster and use Nikon mount glass. MFT is perhaps the easy route as it's small and communicates with the camera. SB + Nikon mount (e.g. Sigma 18-35; AI-s manual primes) is the best investment because you can use them on almost any future camera you buy, the result is more filmic than MFT, and the SB gives you Super-35mm crop and improved low-light. The G6 gives you all the tools you need to shoot with manual lenses anyway (peaking, histogram, etc). Resolution of the G6 is much better than the D5300, and it's easier to use, but in all other ways I prefer the D5300 image.
My 2 cents :)