Right. Second try.

I hope you don't mind Original poster, but with the coming of 'Endwalker', and the new stories being introduced about Garlemald, the back story may be a little outdated. I have an idea for a possible new backstory, though it won't be as well articulated as yours. I fear I'm not very good at writing. I really hope you don't mind... Anyways, here goes... so the idea is this:

These Moogles actually hail from the 'New World', the same place as the Ma Moolja and blue magic come from. Being quite deft and nimble with their hands, they have been able to create wondrous creations out of the materials nature provided. Clocks, windmills, machines; you name it, they probably made something like it, though not to the level of Magiteck the Garleans use, as they don't have the materials needed. Generally quite content to live amongst themselves, away from other races, some have recently been seen travelling far beyond their territories; some heeding the call of adventure, while some wishing to travel and learn of new techniques and technology. Upon seeing them, the other races likened their appearance to that of a Moogle, thus earning them them name 'Moglet' (insert better name here?)

Perhaps these Moglets are descendants of Lopurrets who came from the Moon; this faction wishing to live on the world rather than simply gazing at it. Perhaps they abandoned their duty on the Moon to do this, or perhaps they were banished for some ill-considered deed? Settling upon the earth, over time their appearance changed to help help them live in their new home.

Their brightly coloured Poms allow them to locate each other in the tall forests they live in, and they can fly for short periods of time enabling them easy access going from tree to tree. In recent history however, some have lost the ability to fly due to lack of use for their wings, due to them creating lifts and the like, getting rid of the need to fly.