Ideally a takedown would have both halves around 14" so that assembled it's 26 and a bit and it backpacks nicely. Unfortunately the length of a 10/22 receiver plus a reasonable length-of-pull gives you a longer back half so there's less motivation for a short barrel than you might have in a "solid" rifle built to the 26" spec. Anything that doesn't make the front half longer than the back half is good!
There's maybe the idea of a folding stock plus the TD but I'm not sure that would work out either.