Yes, it is possible to save a PhD in 10 months. It's tough work, but you can do it if you give yourself the chance to clear your head and re-prioritise, if you change the way you handle downtime, and if you have a small sprinkling of luck.
I'm going to get some heat for this, but I can empathise and I would regret not sharing this with you if it meant it could help. This is all from experience and any points I'm going to make are purely anecdotal, a little bit brutally honest in places, with a little bit of dry humour in places. It's the first time I'm sharing my experience like this, and it's a bit of an essay but I hope it helps anyway.
Out of a staggering coincidence, 10 months how long it took to get my thesis done - the end of the final month being the hard deadline. Here's the Gource animation of my git commits to prove it. Making matters worse, I only actually started making real progress in the last month, as you will see, and pretty much everything I had written before that was either majorly rewritten or removed, so for all intents and purposes it was a lot less than 10 months. For complete shameless honesty, two days before submission I had three git commits, with commit messages "kill me now", "WHY?", and "F*** THIS S***". Six commits later, my commit message was "OMG I'M DONE", before the final commit: "oops, forgot the declaration". Yeah, that happens.
I'm not proud of leaving it so late to get started on formalising my work, and I had slightly different reasons - I took on a C++ job during the early stages of my PhD (it grew from a bit of consulting work into a full time role quite quickly) and that took over most of my time, leaving me physically and emotionally exhausted. In the last few months this made it even harder, because it gave me the temptation of an easy out (sidenote: I'm still working there, and I love it - all that has changed is the letters by my name).
First of all you need to take a short break of a couple of weeks to gather your thoughts. It sounds crazy, right? You're stressed out by a looming deadline (i.e. you're human) and a break makes it WORSE, right? No. You need to focus on your mental health, get some exercise, get some nature into you and imagine how it'll feel to be able to do that one day without stress looming over you (or, at least, stress of the PhD flavour). Towards the end of this break make your decision on whether to continue your project based on the old trick - flip a coin to determine the outcome, and if the result disappoints you then turn that coin over. I bet you any money that your choice will be to continue.
The points about the supervisor are unfortunate. My supervisor was a superhero - extremely patient, fought my corner, and generally a really nice chap. However, this is the time when it's rather natural for students and supervisors to drift apart somewhat. They are no longer responsible for your 'supervision' as such , although they should certainly be there to provide guidance if you ask for it. If your supervisor isn't playing ball, then it isn't the end of the world - it's the examiners you have to worry about, and although your supervisor does coordinate things with them, he won't harm your chances. If anything it sounds like he wants you to prove yourself, and you have plenty of time to do that.
I can wholeheartedly say that any advice about getting N pages done per week or writing X section in Y amount of time is to be taken with a pinch of salt - if you're anything like I was, you'll have periods of very little progress and periods of extreme productivity. In my experience, planning regular incremental steps will demolish your motivation when you fail to reach one of those artificial milestones on time. Case in point - if you look at the animation I linked to above, you'll see that I had long periods of inactivity or only minor modifications, and bursts of activity every so often (particularly September. My final deadline was the end of September. No, I didn't do the whole draft thing. That's for sensible people).
You have done a lot of work and you have specialised in a certain field. You might not feel like it right now, but you have done things that no one else has, got excited about something that a fraction of a percentage of the world's population is able to even understand, and the next step is to share as much of it as you can in one coherent document and to try and trick readers into feeling that excitement too.
I'd suggest not writing your introduction first. It's the hardest thing to get right, and the best and easiest way of doing it is to get your content down first and then figure out the best way to introduce it. Many people abuse the intro as a content filler, and as a way of raising the reference count into the stratosphere, but if anything this can detract the reader from the main content. If that's your thing then go for it, but IMO the best introductions are those that give a rather specific overview of the state of the specific area that you're going to present.
Pointers on productivity
So let me end this rant with a few suggestions if you decide to take this further.
- If you don't already adopt a project planning methodology, do so. The simplest option is to start a Trello board. Install the app. Put it as a widget on your front screen on your phone. It will be your life from now on. Don't go crazy on the planning, though - don't spending more time micromanaging your thesis than DOING your thesis, though if you do then you're in for a fantastic career in management.
- If you don't currently use version control, do so. Obviously I'd recommend Git if you're running a LaTeX project. MS Office offers version control if that's your thing.
- You will have periods of low motivation. That's guaranteed. Use them to your strength. If you aren't feeling up to adding new content, there are plenty of house-keeping things to get on with that are essentially brainless - improve formatting of existing content, add acknowledgements and the declaration, play around with the title page, create some figures. If you're feeling pretentious, find some corny quotes to put on each section. You're going to need to take procrastination to a whole new level.
- University libraries usually store previous students' PhD theses. You have every right to access them. Think of some people in your field who completed their PhDs at your university and get some inspiration from their work - how they used graphics, how they formed their introduction, how they broke down their sections, how they concluded their work. Maybe they added toy examples of certain problems and demonstrated their solution, and maybe you like that idea and want to do it too. There is nothing to be ashamed about by getting inspiration from others' work. That's what science is all about. But, obviously, limit that to just inspiration please.
- Think of everything you've done so far. Which part of it do you feel is most important? That becomes the motivation of the entire thesis, and everything else leads up to it. Choose a plan of attack early.
- At all times keep a dream in mind of life post-thesis. This will help you more than you can imagine.
- Get feedback from colleagues. Not so often that they consider you a chore, but don't go it alone and end up going down the wrong path.
- Start a routine. It doesn't have to be a good one, but I'd at least advise (a) a regular eating place - NOT IN THE SAME BUILDING AS YOUR DESK, (b) a regular number of hours sleep, (c) dedicated time with people who you like and who can put up with you being a shell of a human being for a while, (d) a music playlist that provides you with a sense of continuity while working, (e) regular water breaks.
On that last point, my routine certainly wasn't a good one. In the last month I made sure I had at least 5 hours sleep, my regular eating place was Burger King, my dedicated time with people never really happened, and my music playlist was 20 dubstep and EDM tracks I liked on constant and endless repeat, and my 'water breaks' were a six-pack of redbull during the thesis day shift and beer for the thesis night shift. Again, not proud of that, but it worked.
In terms of your mental health, that is your utmost priority. If the stress makes you want to quit and become a park ranger, that's fine and normal (IMO and IME). If the stress makes you angry or upset about anything other than your thesis, quit and become a park ranger. It's a hard and fast rule to live by.