I'm not sure what exact advice I want, so I'll just give my experiences.

Basically, everything was going great until the Viva. My supervisor said I was more likely to pass first time than anyone. The examiners ripped half of it apart and said while 3 of the 6 chapters were comfortably above PhD level, I needed 12 months, in which I would completely restructure the entire thing, with the chapters in a different order and the other 3 completely rewritten, and have a whole new argument from start to end.

I have done this, and resubmitted. And I know that 3 of the chapters are still woolier than the others, 1 of them especially. On the other hand, everything is in the exact order they wanted, while I now have a strong conclusion I'm really pleased with and that demonstrates clearly and vividly exactly what the major research contribution of the thesis is, and which follows on from the evidence provided.

All the stuff is now in the order they want it, and supports my conclusion. So I feel that any further stuff they want done would be editing and tightening the 3 weaker chapters, so they better and more clearly express the same points. Nothing weak about it affects or detracts from my conclusion. I strongly believe that anything that needs changing can now be done in 3 months.

So I'm wondering if it's worth emailing my examiners, saying I felt extremely stressed and unsure about it, and asking them to be as sympathetic as possible. To stress that I believe the conclusion clearly demonstrates what my substantial contribution is and that, if they agree with me, the weak bits in the 3 weaker chapters can readily be sorted in 3 months. I believe also that as they can still fail me if those 3 months of corrections aren't done properly, they don't have anything to lose by being as sympathetic as possible.

Or should I leave them completely alone?

Leave them completely alone. Seriously contacting them and asking them to be sympathetic is a really bad idea. In fact depending on your university's regulations, it might even infringe the examination rules.

Okay, thanks for the advice :) I have definitely thought again about taking that route, and what I would say to them is, I guess, what I would say if I have to appeal.

I concur with bewildered.

Thanks again, I won't be going down that route, then!

Does anyone think a good thing to do would be to go through it with a fine tooth-comb and list the problems I have started to see and show that it clearly would take less than 3 months to fix them, to argue my case if they failed it rather than give 3 months? I have seen someone recommend that approach somewhere else.

Yes that is a good idea, many people do that. I think the general advice is to not give the corrections to them unless they ask for it though, because they may not notice them and then you will highlighting additional weaknesses to them.

Ok thanks, but if that's a good idea that many people do, as you say, then presumably I would then let them know that I had done that at some point?

In some universities, you are not supposed to communicate with the examiners on corrections-related issues.
Perhaps this is the reason why certain universities insist that the identity of external examiners should be kept as a secret.
Bewildered is absolutely right that such email can cause complications to awarding you the degree!

If you look back at your thesis one year later, you will very likely detect more issues.

If it was me I would play it tactically. I would see what they had to say about it. If they seemed like they wanted the corrections I would give it to them. If they just handed me a list of corrections I would just take it and not mention the things I had found.