Those old hand drawn plats are fun. I'm wondering if you are experiencing the phenomenon that I have observed where they will push all of their errors into one area of the plat. On the plats I have seen this, they usually have the correct bearing and distance labeled, but the line is definitely shorter or longer than what is labeled.
I would try entering just that lot with the 100' back lot line and see if it closes.
Does the plat georeference very well?
Jeff Ward
Summit County, Utah