Hey Brother,
I suffered the same sort of thing from writing screenplays (what is it about writing?? :\), and actually posted on another dharma board for help (specifically about procrastination), and they, like another poster here, recommended a non-dharma solution: The Now Habit, which is apparently the best book on dealing with procrastination. One of the main things it talks about is diminishing fear, which sounds like exactly your issue, so it may be helpful.
I forget now how exactly it recommended going about diminishing one's fear, but it seems to me like that actually does have a dharmic solution: for me, at least, the fear came from the desire not just to write something good, but the desire to have a great career and all the pride, money, and respect that comes with it. The fact that you said that "too much depends on it" makes me think that this may be going on with you, too. Basically, can you just let go of the desire that it be any good, or even finished? A therapist once told me, for instance, when I was panicked about the prospect about not getting straight-As, that I had to be okay with getting a B. It really helped lower my anxiety, and I was better able to focus on the material and the love of learning and all that.
Now, if you get rid of the desire for it to be finished, it begs the question: why in fact bother finishing it and getting a PhD? Some will say that you can "desire" a PhD without craving it per se and bringing up a bunch of dukkha and stuff, and I agree, but it still begs the question: if pride and greed are not your motivators for choosing that course of action, then what is? Is it the best means possible for you to make a living? Will your work make the world a better place? Whatever it is, focusing on those reasons--i.e. merely doing your duty to provide for yourself or helping others--will make it so that it's not your entire basis for self-worth that's at stake. (Sorry if any of this is incorrect or assuming too much.) It reduces it to the equivalent of the "desire" to make yourself dinner or volunteer at a homeless shelter, which typically don't elicit such a stress response.
Of course, this is easier said than done. Even after I quit screenwriting (I decided that it was not of value to the world and that I was doing it only out of pride and greed), I nearly went back to finish up a screenplay purely as a favor to a friend and just the thought of doing so revved up waves of panic in me. There's a certain amount of ingrained classical conditioning at this point that is really physiological and won't go away even with the steps I touched on above. In that case, probably my favorite technique to circumvent this is to write something that "doesn't count". It got to the point where even writing in screenplay format made me nervous, so I just wrote stuff out in long-hand so I would feel at liberty to write totally badly, but just to get something out. Sometimes it actually came out good and just typed it up in screenplay form without changing it; sometimes it came out, in fact, super awful, but it was at least in some sort of shape or form that I could work with, and it was considerably easier to spruce that up rather than attempt to write something perfect at the get-go.
Another, sort of similar technique is that I started writing projects other than the big screenplay--just stuff for fun. It kept me reminded that writing could, in fact, fun, that I did, in fact, have the capacity to write flowingly, and that good stuff could result even though I wasn't trying hard. It showed me a mode of thinking that I could then try to duplicate in my "real" writing.
Next (sorry for bombarding you with all these--as you can see, I've dealt with this a lot!)--this is a bit contradictory to the last point, but you know, you throw everything you have at it and one works one day, another works a different day--give yourself to permission to go slow. There are (supposedly true) jokes about both James Joyce and Oscar Wilde going SUPER SLOW; I mean like one sentence per DAY. Of course, perhaps that's a luxury you feel you can't afford given that you say this has already gone on too long, but first of all, better late than never, and secondly, what the stories about Joyce and Wilde tell me is that sometimes good things just take time. I read advice from some no-name screenwriter that one should be able to finish a screenplay in three months, and at first I was panicked (I had only ever been able to finish a screenplay in two years!!), but then I was like, should I listen to some no-name screenwriter or James Joyce?? But even if you're like, no, really, I need to go faster, giving yourself permission to go slow can, paradoxically, make you go faster than otherwise by taking your energy out of whipping yourself over how little you've done and how much you need to do and back onto the material itself.
Sorry if you've already tried all this stuff. If not, hope it helps!