If you go to Google and type in Stratford-on-Avon bed and breakfasts a whole long list will come up.
You have your list of places that have no space, so keep that at your side. You must understand that anywhere listed in Rick's books gets booked up very quickly. I would keep on trying.
The list I looked at included feedback from people on Trip ADvisor. Google is the key to finding just about everything you need to know about visiting most places!!!
Personally, I don't like Stratford and think it is terribly touristy. Most of the historic sites are a bit iffy historically anyway. It is not a quaint cute English village. I never understand why people have to visit so and so's birthplace anyway.!!! Having been to Beethoven's and Moart's (I believe they were their birthplaces..it has been so long, I don't remember anymore!!!)
I haven't visited anyone's birthplace in ages...much more interesting to get a feel of the area in which someone famous lived..if that is still possible due to modern development.
You could also look in neighboring areas for somewhere to stay probably cheaper but not near Warwick Castle as that is a big tourist draw as well.
If the Old Manoar HOuse is part of Wolseley Lodges, that is an organization of private homes that meet certain very high standards and are not inexpensive.
I think I would keep trying but always remember the adage you get what you pay for. And there are so many lovely villages in England in the south to s stay in!