If it wasn't for the lack of affordable glass, I might actually go with sony (eek) if I were to switch to full frame this very second. They have some very compelling cameras, assuming you won't be doing a lot of low-light shooting (which I rarely do). Losing 3 stops of light to their translucent mirror technology is a bit extreme. Of course the A7 and A7R have piqued my interest as well. I already have some glass, so the D800 wouldn't be out of the running either, of course. Considering how quickly the price of the D600 is dropping, that is something I am strongly considering as a cheap way to get into full-frame. I've seen a couple under $1200.
If you want easier workflow, 5DM3 isn't the way to go, because it all but REQUIRES you to do more work in post. The image is horribly soft and you're going to have serious moire issues (which can't be fixed at all). The only reason I'd buy the 5DM3 is for Magic Lantern, which is going to add additional steps to your workflow (and a SIGNIFICANT amount of hard drive space if you're shooting everything in RAW, which is the only way I'd shoot with any Canon these days). You might gain a bit of low-light advantage with the 5DM3 over the D800 and perhaps better auto white balance, but you should be doing your WB manually if you want to guarantee that it's correct anyway. Of course the D800 is pretty soft as well, due to the line skipping...so both cameras could be much better for videographers, imo. If I was doing weddings, I'd just step up to a pro-line cinema camera or camcorder, I wouldn't want the hassles that come with a DSLR. A camcorder, in particular, would make that work a breeze, but you'd need to get a good one, the $300 camcorders aren't going to cut it in low light situations.
I wouldn't hold your breath for Nikon to "fix" the aperture issue. That's been an issue for a long time now, they've released quite a few cameras with the same "issue", so I don't think it's something the company sees as too big of a problem. I don't like it, but it's not a deal-breaker for me, either. I am extremely happy with the image quality that I get from my D7100. I liked the quality from my D5200 very much too. I can cut footage together from those two cameras quite easily. That's something which you may have an issue with if you go with one Nikon and one Canon, they're not always going to match up perfectly.
I think if I was doing professional video work, I'd buy a Canon Cinema Camera or a professional-line camcorder with a beefy sensor. I picked up a crappy little camcorder a few months ago and I've been pretty astonished by how simple it makes things. It's got autofocus that WORKS, it's light and easy to carry around. That being said, there's no way I'd use that thing for professional work, the quality stinks if you go past about 1/4 optical zoom (digital zoom is complete trash), it gets horrible ghosting and chromatic aberration. I can definitely see why people like them though, they take a lot of the guesswork out of the process. It's ridiculous fun to use the full zoom and be able to watch a spider from an eighth mile away, though.
Sony's Z100 camcorder is very interesting, albeit extremely expensive, but having the ability to shoot in 4K would be mighty nice. The VG900 is full-frame and would give you amazing images for weddings (again, quite expensive, but not nearly as much as the Z100). I wouldn't be able to afford those types of things for doing my own piddly little projects, but if I were making money, I think I'd probably only use the DSLR for very specific shots and use a camcorder for most everything else. Sure, a DSLR can give you some truly amazing results, but you have to work very hard to get those results and you'll have a lot of failures along the way. You don't get any do-overs with a wedding, that's a one-time thing, if you screw it up, the image is gone and there's no way to get it back. So for a TRULY easy workflow, I wouldn't use a DSLR at all.
If you want easier workflow, 5DM3 isn't the way to go, because it all but REQUIRES you to do more work in post. The image is horribly soft and you're going to have serious moire issues (which can't be fixed at all). The only reason I'd buy the 5DM3 is for Magic Lantern, which is going to add additional steps to your workflow (and a SIGNIFICANT amount of hard drive space if you're shooting everything in RAW, which is the only way I'd shoot with any Canon these days). You might gain a bit of low-light advantage with the 5DM3 over the D800 and perhaps better auto white balance, but you should be doing your WB manually if you want to guarantee that it's correct anyway. Of course the D800 is pretty soft as well, due to the line skipping...so both cameras could be much better for videographers, imo. If I was doing weddings, I'd just step up to a pro-line cinema camera or camcorder, I wouldn't want the hassles that come with a DSLR. A camcorder, in particular, would make that work a breeze, but you'd need to get a good one, the $300 camcorders aren't going to cut it in low light situations.
I wouldn't hold your breath for Nikon to "fix" the aperture issue. That's been an issue for a long time now, they've released quite a few cameras with the same "issue", so I don't think it's something the company sees as too big of a problem. I don't like it, but it's not a deal-breaker for me, either. I am extremely happy with the image quality that I get from my D7100. I liked the quality from my D5200 very much too. I can cut footage together from those two cameras quite easily. That's something which you may have an issue with if you go with one Nikon and one Canon, they're not always going to match up perfectly.
I think if I was doing professional video work, I'd buy a Canon Cinema Camera or a professional-line camcorder with a beefy sensor. I picked up a crappy little camcorder a few months ago and I've been pretty astonished by how simple it makes things. It's got autofocus that WORKS, it's light and easy to carry around. That being said, there's no way I'd use that thing for professional work, the quality stinks if you go past about 1/4 optical zoom (digital zoom is complete trash), it gets horrible ghosting and chromatic aberration. I can definitely see why people like them though, they take a lot of the guesswork out of the process. It's ridiculous fun to use the full zoom and be able to watch a spider from an eighth mile away, though.
Sony's Z100 camcorder is very interesting, albeit extremely expensive, but having the ability to shoot in 4K would be mighty nice. The VG900 is full-frame and would give you amazing images for weddings (again, quite expensive, but not nearly as much as the Z100). I wouldn't be able to afford those types of things for doing my own piddly little projects, but if I were making money, I think I'd probably only use the DSLR for very specific shots and use a camcorder for most everything else. Sure, a DSLR can give you some truly amazing results, but you have to work very hard to get those results and you'll have a lot of failures along the way. You don't get any do-overs with a wedding, that's a one-time thing, if you screw it up, the image is gone and there's no way to get it back. So for a TRULY easy workflow, I wouldn't use a DSLR at all.