How do I approach a supervisor who seems to be unconcerned with my projected end date?
It sounds like it may be time for you to lay all this out to the director of graduate studies in your department.  Here are some suggestions in case you decide to do so:


You can take a friend with you for moral support if you wish.  
Make an appointment. If someone asks you for a reason, you can say something brief, such as "ask advice about my graduation timeline."  (That's to get you a foot in the door.)
Speak calmly.  Just explain your experience so far, and leave out the part about your fears and how long you've been working on it.  Leave out your conjectures about your advisor's possible motivations.
The administrator may ask you some questions about your timeline and you may, of course, answer them.  
If the administrator makes a suggestion or advises you to do something you've already tried, don't nod and say you'll try that.  Tell him or her calmly what has occurred when you have tried that.
Ask him or her if s/he can get back to you by (name the date that comes up in 6 days).  That way, if you have to go up the chain of command, you'll be able to say, "I met with Prof. YY a week ago."
Document the conversation by sending a thank-you email that same day.  E.g. "Thank you for meeting with me today to discuss etc." and include a bulleted list of the points covered in the meeting.
If the administrator does not commit to getting back to you, you may jump to the next level without waiting.


I think that in most departments a five or ten-minute conversation with the director of grad studies will do the trick and either your advisor will start moving, or the department will find some other way of getting you out the door.