Apparently, I set these spoons aside to look into this further and have just rediscovered them. Here is a link to a sampler from 1828, documenting some if the the lineage of Frederick's apprentice Benjamin Swan (including daughter Charlotte Wingate who is noted on the americansilversmiths site):
https://www.mainememory.net/artifact/13426Benjamin Swan is documented but I add this which was located: 01 Jan. 1797-Dec 1867, marriage to Hannah Smith of Hallowell Maine, "He was a silversmith and was in business with his son Moses Moody Swan (Feb. 26, 1818)". Moses is also documented.
It is reported that Frederick, sometimes spelled Frederic, may have been trained by his elder brother Paine who was a clockmaker known to have been in Boston at one time. Under Swan Family at rocksvillage.org, there is Paine Wingate II (1787- 12 Jan. 1849) whose second wife is a Charlotte Swan (12 July 1794-14 Jan 1855). [I can't attest to the accuracy of these old documents.]
Back to Frederick, a fire swept through Augusta in 1865 (the year after both Mr. & Mrs. Wingate died) destroying a vast number of structures including the third Masonic Hall. But earlier, the second hall had existed in the "Wingate Block" some two blocks north of Market Square on Market Street. This information give no dating, but perhaps this was a property location where the Wingate family conducted their trade?