If you quit on your own terms and took a break for a few months to do something worthwhile, you have a lot less of a problem picking up where you left off. When asked why you left your last job, immediately indicate it was your choice to do so (even if it wasn't exactly a choice), and then explain what you did besides immediately start looking for a job.
At my last job, I ran into issues with my boss. We both agreed it'd be better if I quit. (No employment insurance that way, but I retained positive rehire status, which is more important than people realize.) So I quit, and took the summer off. I published a book on Kindle, and when that inevitably didn't make me an overnight millionaire, I started applying for jobs. I got an interview by the second application, and framed the terms of ending my previous employment as, "My boss and I both agreed the position really wasn't what I had expected it to be. So I took a break, and pursued my dream of publishing a novel. Now that I've done that, I'm ready to get back to work."
On the topic of matching requirements - match them in the cover letter with the qualifier of "I may not have (x) but I do have (yz)" - (x) will get picked up by the HR scanning software, and get it in front of a pair of human eyeballs. Which is really all you need to get an interview if NOBODY has all the qualifications.