I have a wonderful family record in the handwritting of Charles Shaw Adams which starts in detail with Michael Adam, his grandfather and extends through the children of Charles Shaw and his siblings.A chart, which I believe contains errors, shows the male ancestors back to Henry of Braintree, the immigrant.I obtained the copy from the DAR, apparently submitted by someone applying for membership, and I noticed that there is a check mark by the name Augusta Tappan. I wonder if this may have been the source for the information that you have. At any rate, I would like to exchange documents with you and I can provide more information on the ancestors prior to Michael if you need it.
Let me know your address via e-mail and I will send a handwritten copy as well as my transcribed version. The original copy is so poor that it can barely be deciphered.