My son sounds very much like your daughter :) Super fun kids.
We were in the same dilemma. My son's preschool was 5 hours a day, and he was absolutely thriving. 1/2 day Kl in our district was only 2.5 hours long, and had none (NONE!) of the "extra" stuff (music, pe, art, or recess) that was a part of full day K.. which was a bloody 8 hours long, but we didn't want to go "backwards".
In some ways we regret paying the 3k for full day K, which we could barely afford. He was bored, exhausted (physically & emotionally from having to restrain himself...his preschool was Montessori so he had a lot of independence and independent thinking/work was encouraged... obviously that's not the case in public school), and we *barely* got to see him (morning madness to get out the door, a 20 minute commute... then the school was out at 330... but the bus didn't drop him off until 415-420. We were never home before 430, and frequently 445/500. At which point it was either racing off to soccer practice, or cooking dinner/dinner/bath/bedtime.
He had a fantastic teacher, great friends (I've got one very social kid), but he was absolutely miserable. By winter break we knew it wasn't working. We looked into private schools, but couldn't afford the 15k. We were on the fence about whether or not to pull him from school over break, but decided to let him stay to be with his friends.
Half day K didn't make much sense to us (drop him off then turn around and pick him right back up?) but if we'd done it we probably wouldn't have pulled him from school as quickly as we did, because full day K showed us without a shadow of a doubt that this wasn't the best educational option for *him*.
Ironically, now that we homeschool... we pay around $100-200 a month for ALL of his "extra" classes, which I never considered to be extra in the first place. He's in gymnastics twice a week, does soccer/snowboarding/baseball/swimming seasonally, is in a 2 hour long art class, music class twice a week, and does every school break play through the Bathhouse Theatre. We have special science seminars ( the UW has some killer kids classes, like building their own Gallelio type telescope, and every other wed the Observatory is open to the public), and are out and about doing field trips twice a month... all for less than we paid for full day K.
They're only little for so long. Even if your 1/2 day K is ridiculously short like ours, if you want to ease her into the very rigid world of schooling, I would strongly suggest half day K, with whatever "extras" she enjoys and you want paid for out of pocket in your own time and schedule.
So too, remember the 1st 2 years at PS are the "sick" years. Expect to be sick at least once a month the first year (we thought we'd bypass this part since we were in preschool and brought home germs from the university & hospital...doh! Nope. Sick every month). Missing 1/2 day K because one is sick, one misses out on a great deal LESS than missing out on a full day of school. 1st grade is easier (as far as being sick is concerned, the average is every other month). <laughing> And don't think we got out of being sick, by pulling kiddo... most of his friends as well as most of his classmates/sportsmates are in PS.
Everything I'd ever read, said that full day K gives kids a better academic leg up... but I really have to wonder about their samples... our local school's curriculum didn't mesh up with what DS already knew from being in preschool until (at the earliest) middle of the 1st grade, and in some subjects, not until 3rd grade.
In our district the "goals" for K were counting to 20, knowing the alphabet, writing your own name, colors/shapes, & listening to directions. Many kids came into his class not knowing any of this, and it took the full year to teach them. For these kids I can very much understand that full day gave them a leg up... but for kids who already knew that and more, there was little if ANY academic benefit.
:)
Best
Z