I was in a similar boat going into this past application cycle. I graduated with a masters in media studies back in 2012, and at that time I wanted to do anything but another year of school. So I got a 9 to 5. After a few years of doing that and becoming increasingly discontented, I decided in December of 2016 that I'd finally go back and (try to) get my PhD. Of course, the deadlines for applications had already passed, some by just a few weeks. At first, the thought waiting a year just to apply was sort of unbearable. But preparing a solid PhD application takes time, and what I found out is that I really needed that year. I can't say anything bad would come of it, but I also wouldn't suggest asking programs about submitting a late application (especially since we're already in April), if only because you have an opportunity here to show the programs you're applying to that you're really taking the application process seriously.
Here's how I spent last year: I reached out to the Chair at my alma mater in January for advice about applying for PhD programs at the end of the year. She saw that I was serious, that I wasn't rushing into a PhD, and that I was taking time to prepare my applications, and she ended up writing a letter for me. I spent the Spring researching programs, finding people doing the sort of research I wanted to do, and thinking carefully about whether my research made sense with what the field was doing, whether I could/should adjust my research interests at all to that end. Over the summer and in the early fall, I reached out to POIs about my research interests, and I talked to current PhD students to ask what they did leading up to their applications, etc. And I spent the Fall reworking my application materials, reaching out to (and meeting face to face with) letter writers, and getting all the bureaucratic ducks in a row (transcripts, test scores, etc.). And I spent a lot of time feeling impatient! But I'm starting my PhD at one of my top choices this fall, and in retrospect, I don't think I could have done it without taking the year to prepare my applications.