Wow! I saw what you meant about the transcription. It was everywhere, even to the point where the transcription was being quoted as a primary source.
I couldn’t locate the letters but I found some information that may help.
The Library of Congress has online the transcription of Records of the Virginia Company, 1606-26, Volume IV: Miscellaneous Records by Susan M. Kingsbury. In it, she states that Frethorne’s letter was in the Manchester Papers, Public Records Office, London. (The PRO is now a part of National Archives UK.)
The Manchester Papers contain the files of Nathaniel Rich (a shareholder of the Virginia Company). Frethorne’s letters were collected in this group.
According to the UK National Archives website, the Manchester Papers “were withdrawn from the Public Record Office on 15 May 1969.”
VirtualJamestown.org has a list of records used for their project. They mention the Alderman Library Special Collections & Frethorne’s letter. The site mentions what sounds like something other than the original letter. Then it seems to point back to a collection in Kingsbury, England. I’m not certain what repository this is.
If our National Archives can’t help, you might try contacting the University of Virginia (Alderman Library) or Virtual Jamestown to see if they have any leads.
Virtual Jamestown info - The paragraph under Alderman Library, Special Collections section (near bottom of page), with #21 underneath that mentioning Frethorne letter
Link to 1st page of letter transcription
National Archives UK for Manchester Papers
A tiny description
Dear Ms. Cordes,
Thank you for posting your request on History Hub!
The U.S. National Archives and Records Administration does not have a copy of this document. Based on Ms. Yuhasz’s response, we suggest that you contact the National Archives of the United Kingdom to inquire as to the disposition of the Manchester Papers after they were withdrawn from the UK Public Records Office.
We hope this is helpful. Best of luck with your research!