This is remarkable!
Sooner or later the facts behind these old swords come to light.
So the flaming T has nothing to do with Toledo, and it has seemed known that these 'bilbos' were from Basque country, with suggestions of Eibar.
I had always presumed these most commonly went into Cuba, and from there diffused throughout New Spain. Bernardo de Galvez (1746-1786) and governed Spanish Louisiana and Cuba and was Viceroy of New Spain.
The Spanish assistance to the colonists in the Revolutionary War is seldom recognized, but Galvez and his forces were key in interference with the British and supplying Colonial forces.
It seems that most records in the Basque and other areas focus on the production of muskets and bayonets, but as usual no mention of swords.
It seems reasonable to presume these M1728 examples with what you have revealed as ARRIVILLAGA were likely made in Tolosa, probably by Francisco Arrivillaga ? as he worked 1736-60.
Any chance of pictures of the example found in the Louisiana barn? what a treasure!