Small yards, and I have a very small one, are fairly transparent. What you see on inspection is what you get. And because of that, I think, you tend to keep the liveries you do have. It is a much closer relationship. Because you are small the liveries don't have such big expectations. The reverse of the coin is that any horse who comes to me is treated like my own horse, if not better. Yes they pay me money, but yes I will got out at 11pm at night if the weather changes to make sure everyone has the right rug on.
My longest livery was 8 years, and only ended when the pony died. Five horses/ponies have lived out the end of their lives here, and my family and I have been there to support the horse, and its owner, in the last moments - and then to do that worst of all jobs, wait for the loading onto the carcase lorry.
So with low turnover, it probably is more difficult to find a small yard than a medium or big one. Why don't you advertise that you want to be on a small one in your feed merchant/whatever. Somse soft-hearted person may well come out of the woodwork.