It's either impossible, or maybe you can record for as little or as long as 3 seconds, but it can't be both!

5D3.123 firmware, August 24th 2016 build. Haven't had a chance to test the new January 2017 build yet. 14-bit MLV with sound. 'Global Draw' and 'RAW Zebras' on. 'Shutter fine-tuning' used to achieve 180º shutter for 60p recordings. Lexar 32GB/64GB 1000x CF, will eventually get the 256GB 1066x to make life easier!
In the Magic Lantern menu, I have the following selected:
Resolution - 1920x1080
Aspect Ratio - 16x9
In the Canon menu, I change 'Movie rec. size' and 'Video system' to select the frame rate I want. The above is true for 24p, 25p and 30p. By changing the Canon menu options to 50p and 60p, and nothing else, the Magic Lantern menu will now read:
Resolution - 1920x648
Aspect Ratio - 16x9
Once scaled vertically by (5÷3)x, that gives you an image with a pixel count of 1920x1080.
Unless I'm mistaken, that's the best possible 50p and 60p image you can get out of the 5D Mark III. I understand 3x3 binning has been enabled with the newer crop mode, although 50p and 60p is capped to crazy-wide!
I just ran some tests, this is what I got:
1920x648, 16x9 (makes 1920x1080) 50p: ~ 400 frames, 8 seconds real time, 16.5 seconds playback at 23.976p
1920x648, 16x9 (makes 1920x1080) 60p: ~ 250 frames, 4 seconds real time, 10 seconds playback at 23.976p
1920x576, 2:1 (makes 1920x960) 50p: ~ 700 frames, 14 seconds real time, 29 seconds playback at 23.976p
1920x576, 2:1 (makes 1920x960) 60p: ~ 300 frames, 5 seconds real time, 12.5 seconds playback at 23.976p
1920x490, 2.35:1 (makes 1920x817) 50p: ~ 3000 frames, 60 seconds real time, 125 seconds playback at 23.976p
1920x490, 2.35:1 (makes 1920x817) 60p: ~ 550 frames, 9 seconds real time, 22 seconds playback at 23.976p
Didn't bother testing 1920x482, 2.39:1 (makes 1920x803). Theoretically, a few more frames than above.
While we're on the subject, I really wish there was a 1920x480, 2.4:1 (makes 1920x800) option, ideally in both slow-mo and standard frame rates, please. There's really no such thing as "2.35:1" or "2.39:1". Most modern movies in that sort of aspect ratio are 1920x800, which is precisely 2.4:1. It may potentially offer a few more recorded frames per shot in slow-mo, and a few more seconds of footage on a card. But perhaps most importantly, 480x(5÷3) is exactly 800, resulting in a perfectly accurate vertical scale, just like 2:1 and 16x9. If any developers are reading this, I'd really appreciate this addition, thank you!

Obviously these record times are nothing spectacular, and definitely make things difficult when the camera is mounted on a gimbal or when shooting live event stuff, although you could also drop the resolution too. But for me and what I shoot, it's perfectly workable!
