Since you are a close match to other Kings, it is unlikely that there was a non-paternal event (NPE) in your lineage. In genetic genealogy, an NPE refers to a son's (or possibly an unmarried daughter's) use of a surname other than that of his biological father. It might be due to an informal or formal adoption, out of wedlock birth, name change and other reasons.
It is possible that the Masons could be biological Kings. If their lineage ends abruptly at a time when there were good records and there are few other matches, it might be a possibility. However, it could just be a random match. A lot depends on the haplogroup.
It is very difficult to pursue matches with other surnames. About all you can do is search both surname boards with the other surname and Google the two names together. Before doing a lot of research, it is a good idea to upgrade to 37 markers.
We had a case where a person with a not too common surname did not match any others. His documented ancestor just appeared out of nowhere about 1800. He matched 37/37 with another surname, but it became 63/67 on upgrading.