From what I've seen deer counting, no matter who does it, seems to be wildly inaccurate. I wonder if simply measuring the impact of the deer isn't a better method as if you come up with some reasonable metric then you may be able to establish if the deer are having a negative impact upon the area where they live? In the end that is all that matters, the exact number of deer doesn't seem so important compared to the actual impact they are having and I guess you could consider the landowner's wishes as part of the impact?
I know of one high fenced area that held some "pet" red deer but was to be planted for forestry so they wanted to shoot all the deer but first they wanted to know how many would need shot. I don't know how many were released into the enclosure when it was built. They brought in a local university who counted and measured and studied and declared how many deer there were in the little enclosure and last I heard from the project they'd shot twice as many as the experts said were present, and were still shooting them. This was in a small fenced area with no deer moving in or out and with only a relatively small number of deer present.
