I photographed (or rather my girlfriend photographed) the above page in "Registers of Naval Guns, 1842–1900" (National Archives Record Group 74, Entry 112, Volume 1).
If the print is too small to read, it shows that IX-Inch Nos. 678, 687, and 688 were part of the batch of 20 sent to Sackets Harbor in 1864. They saw no service until shipped to Mackinaw City in 1909.
Guns which did serve aboard USS Hartford from her commissioning until the 1880s can be seen in Cheboygan, Petosky, and Gaylord in Northern Michigan. (As well as in Harford, Connecticut, Vallejo and Mare Island, California, Freeport, New York, and Grinnell, Iowa.) The guns which I have posted thus far can be found here:
https://www.santee1821.net/preserved-artillery/tag/USS+Hartford
As far as the Bureau of Ordnance Records go, I've put up all the relevant pages (to Civil War guns) of Volume 1 of the Register on my website. Volume 2 will eventually come. Volume 2 is actually the earlier book - and it is an utter mess but occasionally has wartime information that Volume 1 lacks.
I've also photographed all of RG74 E111 which lists armament by ship from the 1840s to about February of 1863. Still need to organize those!
Anyway, what I've done so far is here:
https://www.santee1821.net/buord-records