The mystery has been solved! Kudos to Edward Duffy for exceptional detective work in finding the answer. We want to thank all of you for your input and suggestions. The mystery woman is none of the women we thought it could be - not Edith, Helen Bones, Mrs. Peck or any of the others - her name is:
Philena Fobes Fine
Philena Fine was the wife of Henry B. Fine, a close friend and ally of Woodrow Wilson who appointed him Dean of the College at Princeton. Philena and Henry Fine entertained Wilson for tea after he cast his vote for New Jersey Women's Suffrage.
These two news articles were the key to solving the mystery: