Extremely Rare Book

Hi,
I have a book I've had for many years. I've taken it to Chicago for a book appraisal and they found a book close to mine but not identical.
I've sent pics to the National Library of Congress and received an email saying I can not possibly have a copy of this book because they were never put on the market. They proceeded to tell me not one copy was ever sold of this edition because they were all lost in the Great Fire of Chicago when the WW Kimball Co where it was published was burnt down. They then wanted to see the book in person and basically accused me of photo shopping the book into my hands!
The book was later taken to the Chicago Historical Society and they were shocked I had a copy and ask if I'd be willing to Donate it to the museum there. No, I did not donate it. I am still researching for a value.
The book is: Whitney's rapid method for the piano forte. By WW Whitney Published by WW Kimball Co in Chicago. American fingering, Full Complete Edition. originally priced at $3.00. 1st edition Copyright A.D. 1886,
There ARE other editions later done in the 1900s, one even being in two parts. So if you research this book you will find these other editions but I highly doubt you will EVER find this exact one unless mine shows up in Google!
How can I get an honest appraisal for this ONE of a kind book that the library of congress says I CAN'T POSSIBLY HAVE?
I DO have pics but not sure how to put them here as I am new to this site.
Thank you
Laura Kling