You may want to search your local library and used book stores for the "original" (old edition) Square Foot Gardening book. A much thicker book with, I believe, a white cover. Mel goes into all sorts of detail about working with, amending, fertilizing, etc. your native soil. If it's good soil there's not many reasons not to use it, although I sure haven't missed all those weeds. If the soil doesn't look good then the new method, with the raised boxes and "Mel's Mix" will be much better and easier (I used and loved Mel's original book for many years, but when it disappeared in the moving around surrounding my divorce, I ended up getting the new edition and building a new style SFG at my new home, and then at my parents' house. It was MUCH easier.

It sounds like you are well started with a good supply of compost. If you are going to work "in the ground" I would recommend not just adding compost and other amendments (vermiculite was the best thing I ever did for/to my original in-ground SFG) and mashing them in there, but actually removing some (when I say "some" here think closer to "half" than any smaller number) of the volume of soil and replace it with compost, vermiculite, etc. don't try to "mash it in." The goal is to create a light, friable, soil that is easy to work in and for plants to grow in, not stuff a more dense mixture into the same amount of space.

That brings me to the second important thing, which is to plan some kind of walkways, of boards, concrete pavers, etc if you want any paths into your beds. As long as there is room to move on both sides of the bed this shouldn't be a problem with a 4 foot width, but if it is going to be right against a wall or fence you will need to plan some way to get to your back squares without walking on the soil. That's the other big thing to the SFG method, never walk on the soil. That way you can work on it regularly, with light tools (trowels, a spade at very most) mixing in fresh compost every time you pull old plants out, and never have use heavy equipment on the soil again.

Typically the tall plants go along the northern edge of the garden, so that they don't shade the shorter plants.

Tilling isn't necessary for lasagna layering. In fact, the sod is the first layer. Tilling can also do in a large number of worms. So give it some consideration before tilling. My tiller sits in the barn gathering dust.