I've a beachtek DXA-4 XLR interface which was designed for use with video cameras like the Sony VX2000 and FX1 etc.
I've recently sold my FX1 and so this is going to get punted.
It has a VHS pin which would be easily removed with a sharp pair or pliers or small hacksaw, then it'll bolt straight onto a 5D3.
It's a pretty basic unit, it gives you 2 x XLR inputs, which can be switched between mic and line level, and have rotary level controls, on each channel. The device can be set up to work in stereo (seperate audio on each stereo track) or mono (same on both stereo tracks) and connects via a 3.5mm jack.
It does not provide phantom power, so you'll need a hot mic like a K6/ME66, or a line from a mixer.
This will let you record XLR audio in the camera, in the one file along with your video, no synching, no forgetting to hit record on a second device, no charging, no batteries to run out.
This will of course work on any DSLR, however I recommend for use with a 5D3 as this has the headphone monitor from the camera, so you can keep an ear on sound.
I'm the UK, and am open to offers, no matter how ridiculous. The current equivalent is the DXA-2T which sells for around $180us and £160. The unit is very lightly used and in full working order. I'm going to put it on an auction site in a week or so, but thought I would run it past here first.