How to finish my PhD dissertation before funding runs out?
Here are a few ideas, hoping to help you get unstuck.


My spouse had a big-name, brilliant advisor who was impatient and rarely had time to meet with his students.  Fortunately my spouse found a person in the department who was able to be the mentor on the ground, the person to go to when a question came up.  He had a positive, supportive attitude, and was very knowledgeable, but was not able to be the advisor of record because he didn't have the right sort of title.  Perhaps you could find someone like this?  It might even be an advanced grad student or a postdoc.
Suppose your advisor is out of town for a month, but you and he still want to have some collaboration.  A good way of doing that is by writing a weekly email to your advisor, where you make an itemized list of what you've been working on and what questions you have.  I would suggest that you try writing this type of memo even when he is not out of town, and sending it to him the day before your meeting.  That can provide a helpful structure for your in-person meetings.
It sounds like you would benefit from having a study buddy.  This is someone who will listen to your troubles supportively from time to time, and help you stay on track with your goals.  It doesn't need to be someone you enjoy going to see a movie with -- this is similar to a study partner for a particular class, that you compare homework answers with.  Ideally this would be a mutually supportive relationship.


I would also suggest that you bite the bullet and resolve to spend some time learning the background material necessary for a productive collaboration with your advisor.  You don't have to continue working in that particular area your entire life -- you just need to get this PhD done, and it sounds like that's going to be the easiest way to do it.

Reassurance: it will probably not take as long as you fear it will to learn that background stuff.  Although you might not realize it, you are a more efficient learner now than you were a few years ago.  Also, I think you are motivated now to figure out how to do things methodically.

I can see that both you and your advisor have had your frustrations with each other.  I predict that as he sees you taking steps to meet him halfway, you will start to see more patience and a more positive, supportive attitude from him.