In terms of availability at your Home Resort, booking 14 nights at 11 months will be as hard as booking a 7-night or even a 2-night stay at 11 months. How competitive that is will vary by the resort, time of year, and room category.
You're correct you can only book 7 nights at exactly 11 months, but once you have the first 7 adding the remaining 7 is really easy. Every few days just modify the reservation to be longer, as once you have the first night of any reservation booked at exactly 11 months, adding the remaining dates is almost always assured (caveat: rooms going offline for various reasons, including refurbs).
As for non-Home Resorts, 14 nights of continuous availability at the 7m mark will be much more difficult to find, especially in studios (except SSR/OKW, which might have availability).