"Laputa's origin" is possibly Jonathan Swift, since he wrote Gulliver's Travels. So this could refer to something named Jonathan and/or Swift.
Laputa is "a fictional flying island or rock, about 4.5 miles in diameter, with an adamantine base, which its inhabitants can manoeuvre in any direction using magnetic levitation". Aviansie are known to drop Adamant bars and are said to be the best of smiths, along with the Imcando Dwarves.
It could also mean Balnibarbi, the surface-bound island above which Laputa floats in the novel.
This can be a further reverene to the homeworld of Armadyl and the Aviansie: Abbinah. Which as a solid core (Balnibarbi) and islands flying above it (Laputa), crashing into each other.
The "batten of wind provides inspiration" could refer to harsh and windy contiditions on Abbinah, which could have shaped the Aviansie both in spirit and in body.
"Edgar's bird" is most likely a reference to Edgar Allan Poe's poem "The Raven", which is the screen name of a content developer, Mod Raven, suggesting that he is developing this project. Mod Raven's project around that time, which was put on indefinite hold, was a quest known as "Rite of Passage".