Not having a kindergartener let alone a 2E kindergartener I probably shouldn't comment -- but I do have a fair number of reports on kindergarten in VA from friends, some teachers, and they pretty much agree it's a "academic" experience with rules and sitting at desks in rows doing 20 minute blocks of one thing and then another on the teacher's schedule. I put academic in quotes because it's only academic if one is actually at that level, of needing to learn how letters sound when they get combined, etc.
I would, if it was me, file an intent-to-homeschool form for this year rather than a delaying-kindergarten letter, then I would jump the few hoops for that and send them to any school I chose -- perhaps something where they could progress academically but leaving enough time for ABA type social skills time. A private K if I could afford it. A mixed age Montessori half time perhaps with the other half of the day ABA type social skills work? Or a combination of schools, like your preschool plus a homeschooler's one day a week type school with interesting classes to help with getting used chair sitting but in a less restrictive environment where the end result didn't actually matter at all (ie where no one decides to hold them back because they don't follow directions, etc).
Then next year if sending them to K seems ridiculous, if they've made social gains too, then send them to 1st, you will have some tangible evidence from the home-school K year (or from a private/alternative school K year) to show they should be going into 1st. On the other hand, if in a year they are still struggling socially and aren't bounding that far ahead academically then maybe K will a good fit overall with accomodation for the gifted side.
Lastly it may be a little hard to make a exact analogy with your own or your DHs experience. In Fairfax the norm is red-shirting and most kindergarteners are academically prepared as well as a bit older than one would expect. There are likely some very bright, very socially apt, very prepared kids going into K this year, kids who might well do okay in 2nd grade if placed there. Their parents happily send them to K knowing they will win the spelling bee and so on and get into the Fairfax gifted high school and then into a good college. Many bright kids your daughters' age will start K next year.
Polly