My oldest just turned 5, so I guess we may not technically count as "homeschoolers" yet, but...
I, too, am an unschooler. Well, a regimented one, lol! I have a basic idea in the back of my mind of where I'm headed, and then work on getting there a little at a time. Most things, though, the kids really do teach themselves. For example, my 4 year old (now 5) taught herself all about telling time (digital and regular clocks), and how to read a calendar through a series of questions she asked on her own over the course of two or three weeks.
We are not going for a shabby education, either. I think that people often associate homeschoolers with either being ridiculously strict and all over the books all the time, OR lazy and not really teaching their kids anything. But, the middle is actually true. My 5 year old learns lengthy Bible verses, poems, etc by heart. She's able to recite more than 100 different things now, and can speak several phrases in French and Spanish. She can do basic addition, and subtraction, and even some multiplication and division. She is aquainted with a good bit of good literature, and is coming along quite nicely with her reading. She knows where quite a few countries (25+?) are on the map, and can tell you the capitals of quite a few states. She has a good grasp of history, especially of the Revolutionary War, and the 1800-1900s. She is learning to play piano. She understands the basics of electricity and magnetism, and can tell you lots and lots about space. She can tell you names and dates and tons of facts about the moon landing, and details about most of the planets...and on and on. She is easily on a second grade level on most things, reading and social skills excluded. She is not an uncommon homeschooled/unschooled kid. It just happens. Just expose them, and they will learn.
If you make a list of what your kids have learned without you directly teaching them, you may be shocked at what they know...and realize how informal and easy "school" can be.
I believe that they need to be in the habit of making themselves sit and learn something/do something they don't want to do. It's a good skill, but there's time to build it up since they are still young. Daily practice of some sort of the "three R's" is beneficial, but doesn't have to be regimented.
I have a long list, like I said, of things I want to teach her this year, but almost all of it just happens. The more the discover that they are free to discover, the more they do on their own. I have compiled a lot of songs, games, etc, that teach through play, and even my 2yo picks up a lot of it. My kids sing and dance and run around the house in Spanish...and then speak to the waitress at the Mexican restaurant with fair decent pronunciation. We read lots of varied books, and I supply lots and lots of books about their current interests. I just sorta make them "appear" on the coffee table. We talk about math all the time...how many crackers each kid gets, or how many you have left after I eat two.
We write letters and color pictures for friends and family. We sing songs of countries and capitals in the car, and I mention earthquakes as they happen and we find where that is on the map. We talk about the people who live there a little, and then we talk about their feelings, etc. Everyday examples give TONS of real life learning with not much trouble at all.
As far as how to work it in with the EDD, I'm not worried at all. School is life, and we'll just keep going. It doesn't start or stop, it just is. Some days are more, some days are less. I may read fewer books, and forget to hit the three R's in some way for a bit, but that's okay. We'll work it out in the long run.
So...don't stress the formality. The best educations don't come that way, IMO. It's forced and unnatural. It will be deep and lasting if it's just encouraged as it comes. If you NEED something formal, though, try ABEKA. (Christian based). It's about as formal as it gets, but I hear you can get through it in about 2 hours a day. Maybe you can start there, and then transition a bit (if you choose?)
Hmmm...I just reread this before I posted and it sounds bossy and cocky. That's not the point at all, but I can't think how to say it better. Just that...it's easy to feel that you aren't doing right by your kids when you don't "school" them, but that in reality, often times it's easy to teach them SO much without the trappings of school. If you can let that go, then a lot of the stress surrounding it may go, too.