In order for any of the rental brokers to make a booking, there are two things that need to happen. 1) DVC needs to have availability in a given room type for the dates you desire. 2) They need to have an owner with enough points to make your desired booking who has asked the given broker to facilitate the point rentals.
Every broker has access to the same sets of rooms on the back end, but usually has access to different points from different owners. Since you are trying to book BLT at 11 months, you need to find a broker that owns enough points at BLT for your booking. Broker A may not, but broker B may. When you get to the 7 month window, owners can use their points at any resort, which means the brokers have much more flexibility in linking owners with renters. However, at this point owners who own at a given resort have had 4 months to make a booking, and now people at all the other DVC properties (including those offsite) are trying for the same rooms, so more popular resorts may be much harder to book.
Some brokers may try to rent out existing reservations, but that usually happens much closer to the travel dates as owners may be within the date where they can't get the points back.
Booking straight through Disney will be much more expensive then renting points. Yes, if the website isn't showing any availability for those dates, then they won't be able to make the reservation direct.