The Enki K has (adapted) fairy tales, folk tales, and nature stories. Both the fairy and folk tales originate from around the world. The fairy tales have been adapted, if need be, to best suit the development needs of a 5-ish year old. The nature stories are arranged by season. We have been a little disappointed with the nature stories because in no way do they resemble our seasonal changes or weather. (We live in coastal CA ... this last year we ended up with 2 1/2 inches of rain and any snow that fell in the mountains - we can see the snow-capped mountains in the winter - melted within a day or two.) It was really weird reading about King Winter when it is sunny, dry, and upper sixties outside.
So, we don't do as many of the nature stories as we might if we lived where there were definitely four distinct seasons. That said, we love the folk and fairy tales. I waited until almost spring to begin the fairy tales with ds#1, and he really enjoys them. And there are so many to choose from that most every week I was able to find something that really clicked with ds (especially if it was a story about brothers or siblings as ds has two younger brothers).
In regards to quiet time - we don't do it as suggested/structured in Enki. It just doesn't work well for us. But, that is also something I really like about the Enki materials ... you make them fit your family instead of trying to artificially fit your family into a curriculum. We are more mainstream, probably, than most Enki (and by extension Waldorf-ish) families. We watch TV and use the computers, including my boys. A lot of time, our "quiet" time in the afternoon is snuggling on the couch together watching PBS Kids. It works for us, yk? Sometimes we'll put on books on tape. Sometimes we aren't home because ds#2 has speech therapy. Next year, with the baby hopefully being down to one nap a day, I'm hoping we might have a bit more consistent of an afternoon "down-time" but I don't know. Our rhythm is nice to have, but it is completely dependent on our speech therapy for ds#2, and ds#3's napping (which is highly inconsistent) schedule. I found out early on that it was not worth my extreme anxiety/stress to "make" everyone be quiet for that time in their own rooms ... so we don't do it.
And personally, I think financially doing a combo K/1st with Enki is extremely expensive. Yes, I agree that there is a lot more to Enki than just academics; that is the biggest reason why we spend the money on the curriculum. But, for a 6 year old who just finished a half-day kindergarten (Waldorf or not), I think another entire year doing Enki K, especially if delayed academics isn't something that sits well with the PP, is a bit much to expect. As we have both said, Enki is so flexible that one could purchase Enki 1st, and use it over a two year period if so desired - spending one year on only the language arts/SI, and the second year on the math/SI/recorder. It can be started slowly and then sped up over the course of the year. It could be done over the course of 12 months instead of a traditional nine. Just my two cents.
Oh, and Sally, if you aren't sure about the academics/involvement of Enki 1st versus doing Enki K next year, another option might be Oak Meadow K ... it is kind of an inbetween of Enki K and Enki 1st. You won't get the depth of information you would get with the Enki ... but you could buy the Enki Movement/SI binder for Kinder to supplement. (Feel free to ask if you want any more information on using OM and Enki ... we use both.)
And Heket, the foundation guides for Enki are really good and really heavy (in terms of reading ... ). Do you have The Heart of Learning from your OM PreK? After reading the Enki foundation guides, I read the OM HoL book - it was like the cliff notes I needed for Enki.
I would suggest with your dd only 3.5 that you either do the foundation guides and/or buy the Early Childhood guide ... it too was a bit more of a condensed version of the bigger foundation guides. The FG give a very good feel for Enki on a whole, but also contain stuff that has more to do with teaching 1st grade and above. Though I absolutely love the SI part of the FG. It's a toss, but since you have a year and a half or so, you might get more starting with the Early Childhood guides and then mid-year this year (or around the New Year), get the FG and read through those during the spring/summer.