Possibly. But, what do you really lose by trying, or by even contacting somewhere like David's and seeing if they could hook you up with 2 different owners. It would cost much less than renting through Disney.
If they couldn't fill it, THEN you could contact Disney to rent the Villa. I do not think that Disney will really need you to book 11 months out, if you are renting from them. They often seem to be able to come up with rooms up until the last several months.
Or, how about this, do BOTH things! If you are renting from Disney, you don't have to wait until 11 months. I often make rental reservations with Disney more than a year in advance. They put a small deposit on your credit card, but it is refundable. You could do this and THEN you could ALSO try to get an owner to book for you. If they are able to come through, you get your deposit back. For our trip next October, I booked through Disney (for rental) at TWO DIFFERENT RESORTS, more than 12 months out. And then I got DVC rooms, using my points, at THREE different resorts, at 11 months out. Why so many? Because there are going to be at least 12 of us traveling, and POSSIBLY as many as 14, AND, at such a far out time, and not being sure exactly WHO would be going, I WANTED TO KEEP ALL OPTIONS OPEN, until we could get closer and finalize the plans. Then, I will just cancel the Disney rental rooms that we were not going to use, and drop the DVC rooms we decide not to use. It won't cost me anything except a deposit on my credit card for the rooms we rented from Disney, and I will get that back (actually about $2000 back on my credit card) once I cancel. So, again, why not do both?