The Coursera Stanford  and Princeton  courses start again soon, February 20 to be exact. Not sure which one is better, but to refresh my atrophied CS skills of 10 years I've joined the Stanford course. Not sure how it compares to the Khan Algorithms course. Anyone have any feedback?
I think it's a great idea to study algorithms and math for CS, and that OCW is a very good resource. Also consider taking a Coursera course on algorithms. One taught by Tim Roughgarden started Aug 8.  I haven't taken the class, but I've met Tim and seen him talk. He's both extremely intelligent and a dynamic speaker.
I wouldn't prepare specifically for the interview yet. I know that others are very skeptical of the algorithms interview, but I conducted it myself many times, and I'd like to defend it. When done right, the goal is to see how you think about algorithms. I didn't care about whether you jumped to the solution as much as I wanted to hear you think out loud.
My goal was to decide whether I could see myself developing a new algorithm with you as a peer. For many interviewees who lacked a former CS background, the answer was clearly, "No." You need to have a basic and intuitive understanding of Big-O notation, and you need to be able to develop an algorithm yourself. These courses will teach you exactly that (though you absolutely must do the problem sets as well).
Now, it is true that the interview process has its own quirks. So, get experience. Apply to a bunch of jobs, and try to setup interviews with other companies before you even have a phone screen with a company you really want to work for. As with developing algorithms, nothing beats experience. However, I really believe that this step should be secondary to learning the fundamentals. They truly are the basis for the rest.
I viewed classes from all three mentioned above and found Prof Sedwick's classes to be very structured and to my style/liking. Prof. Roughgarden is "free flowing" and may require fast thinking to follow him. Prof Demaine's classes gets very mathematical and I found myself sometimes lost in Greek symbols. But Prof. Demaine is very thorough in building the theory.
 Prof Sedwick: https://www.coursera.org/course/algs4partI
As @carise said, the content may be gone after June 30th and if you want to download, you can do so using coursera-dl tool
 Prof Roughgarden: https://www.coursera.org/learn/algorithm-design-analysis
 Prof Erik Demaine (MIT OpenCourseware): https://www.youtube.com/playlist?list=PLUl4u3cNGP61Oq3tWYp6V...
There are videos of MIT's Prof Erik Demaine's Intro to Algo's from various semesters. I think any one should do.
I'd like to echo the sentiment that quitting without an offer in hand seems like a risky idea. The extra time to prepare for interviews can definitely look appealing, but plenty of others here have outlined all the ways quitting prematurely could work against you, so I won't repeat that here.
Instead, since you don't have a formal CS education, I'd recommend checking out an online algorithms course like this one: https://www.coursera.org/learn/algorithm-design-analysis/hom...
Practically speaking, like it or not (and trust me, I don't), programming interviews tend to involve a lot of algorithms and data structures problems, so having "never really thought about algorithms" puts you at an immediate disadvantage compared to other candidates. Plus, gaining a grasp of the basics of algorithms and data structures is going to be worthwhile regardless as it will make you a better developer.