I could suggest opening up the book by Hamilton showing a number of handle material types for this type of militia sword but you might also take a closer look at the pictures shown so far. Looks like dirty bone to me. There were grips encased in silver sheet. There were black horn examples, bone, ivory, plated brass. It may still not be Ames at all and further pictures of the etch would show that (along with any fraternal connection, as found with the nco form and pre civil war 1832 artillery examples).
As far as I am concerned, the poster was a hit and run likely not to return once "helped out". As such I hate to waste my own time in posting a lot of pictures and writing the entire content of the book but might further suggest you may be mistaken in reading those views of the grip as metal. The poster could confirm that, certainly.

Odd they would not mention that if it were metal.
Note the crack and chipping in close observation. Both bone and ivory pick up color from whatever polishes it and natural light in photography would help. All that is shiny is not always cast metal. Again, these are not solid grips bored through for the tang. Some are truly empty shells with plugs of wood on each end, or like my example, missing an overlay of sheet metal.
At any rate, there is not any noted use of this officer variety for fraternal use, with others already mentioned as so. Any of the the other two patterns etched for fraternal use show the fraternal use.This is not to say that any sword may not have been etched or decorated for society work or have a society connection.
Neither specifically Masonic but both with Masonic imagery. The smallsword one of several given for service to king and country and the other simply a yeoman cavalry officer sword.
Cheers
Also a fwiw. I in no way claim to be an expert on Ames or fraternal swords but I do watch both fairly closely with more than 700 files in Ames folders and about 600 files of fraternal swords in a dedicated folder. The helmet heads in more than one folder, some in Ames files another 400 or so files in another dedicated folder of helmets and other closely related militia types. Within that folder are another 600 files that are not so specifically similar. Eagle pommel swords? More than 6,000 files, so you can see where other interests may be more important. Well more than 12,000 files between all swords, knives, axes, other weapons.
Then of course, are the books and my own collection of material swarf encompassing swords and weapons from the mid 18th century to date.
What do I know anyway?