The world of camera's with 1080 to 4k video does open up options. However what I find is any video footage really needs to be massaged in some form of post processing. The canon L lenses will rattle as it auto focuses and will be caught on any external rode mic on the camera bodies hotshoe. Using external mics on a boom or remotely locating mic is more ideal if your sticking with L lenses. Canon STM lenses are decent but still not L lens quality and zooms are variable aperture.
I did a quick nasty relocation of my rode mic for my 80D. This was simpler than adding audio in post using a tascam or zoom mic. Rode mic does a very good job in sound quality from a 3.5mm jack.
Drisley you've been spoiled with the battery capacity of the 1D series. This is where you get spoiled and take things for granted.
Even a Sony A6500 will be in the 1900CDN range!!! The A6300 is $1350CDN. However the image quality of the newer crop sony's are impressive. If you've tested an A6300 you'll notice a huge improvement in high iso capabilities of the sony crop sensor over the 1dmk3.
The tough thing is that you'd like 4k video capabilities. If your stationary with no AF required or slow moving subjects you can use pretty much use any 4k capable camera. I wish taking video was that simple though

If you do go the mirrorless route I think you'll need to have a pocket full of batteries to keep up with the amount of photos you shoot.
I guess IQ will be the determining factor in selecting a camera as well......
I'm really curious in what you'll be buying. If I was willing to jump on board with a new camera system I'd be debating about a lot of things. The fuji X-T2 with 16-55 f/2.8 and 50-140 f/2.8 would be on my list. Shoot the 4k video with a fuji film simulation preset and have pleasant video straight out of camera.
If I kept with Canon the 5dmk4's 4k would not be ideal. However your stills would look killer with your current glass. $4500 CDN is a hard pill to swallow!!!
I appreciate my 5d3 and my 80D is my 1080 video rig and can be used as a spare body. That was my "logical" decision for wanting decent video with the DPAF 80D. I can have 1/2 hr clips and fill up a 128gb card with no overheating.
It's really hard to get 1 system to do everything you want while meeting every criteria you have on your preference list
