Right ledge method
Associated movies
In this method you fall to the near right ledge from the V and try to stay on it. From there you can move along and drop down at a safe spot of your choosing. But even if you don't quite manage to stay on it, you can still survive a slide off the ledge if you're lucky. Suitable only for PAL.
Full description
Get to the bottom of the V and face right. Run out of the V almost parallel to the cliff face, and try to stay close to the cliff face as you curve round rightwards. The cliff bulges out a little and you should try to get around it without getting bumped away. Two thin triangles of ground join the top of the chevron feature to the cliff, and you need to land on the tip of the far triangle (which is darkish towards its tip). It's just possible to reach it. It takes a bit of practice to hit there because you need to have enough forward speed and you need to arc in towards the cliff a little, yet you can't run off the V from too high up or you'll be killed. It's a matter getting the balance just right.
Crouch as you land. If you're in the right area you'll take a juddering impact which takes a lot of your speed off, but you'll still be heading off the ledge, so you need to try and stop yourself by running away from it. If your luck is in, you end up still on the ledge - though you'll probably be down to only one bar of health. From there you can move along and drop down at a safe spot of your choosing, as described elsewhere.
A bit of extra advice. In heading down to the ledge, I'd recommend facing pretty much in the direction you're going. In that case you'll end up trying to run backwards to stop from sliding off the ledge. If you prefer however, you could rotate right to some extent as you come down, so you'd end up running sideways or forwards to stop from sliding off. Whatever you feel most comfortable with. I prefer the former as it simplifies the work on the controller, and I felt I did better that way.
If you don't quite manage to stay on the ledge, you're still in with a chance of surviving, especially if you end up falling practically straight down. The cliff curves gently outwards and it's sometimes enough to leave you alive, even if you were down to only one bar of health. It's very fickle though.
Checkpoint advice
To make things as easy as possible for repeat attempts, get a delayed checkpoint when ready to start your run off the V.
Difficulty and system differences
As a PAL user I consider this method quite difficult and painful. You have to get things just right and it needs quite a bit of work with the controller. I can get a success rate of around 25% on a good day, but it takes real effort and isn't very enjoyable.
Originally I thought the method might be viable for NTSC and PC too, and could even be easier due to greater powers of drift and greater traction once you land. However, what I didn't realize at the time is that MC is way more fragile when it comes to landing. Here you're landing on a fairly level bit of ground, and even with a well-timed crouch I don't think you'll be able to survive.
History and links
The origin of this method is unclear to me but there's a forum post from December 2002 which I suspect refers to it. It's rather vague but seems to match, especially the bit about being left with only one bar of health. xbill's left ledge method had appeared in April 2002, and I'd guess that various people subsequently tried doing something similar on the right. Especially frustrated PAL users perhaps?
By accident I found the method for myself while attempting the right cliff base method, which I'd seen in Scurty's AotCR Bridge Fall Shortcut (2) video. I was trying to hit the ledge right, and one time I found myself actually stopped on it, still alive. Big surprise! I was recording my gameplay at the time, and from the footage I could view the magic spot I'd hit, which had enabled me to stay on. I refined things from there.
You can see the method used in the first half of BCM12 and also the first half of BCM13. BCM12 also includes two examples of not quite staying on the ledge yet surviving anyway (starting at 2:39). The second of those survivals is pretty freaky (I'm amazed I didn't die), though that actually happened more than once. The movies were advertised in the HBO forum here.