Your theory sounds very much like something Slurpeez, Phee and I eventually came around to early this morning in this thread: https://oncepodcast.com/forums/viewtopic.php?f=91&t=3844&start=50 (start on page 6 for the Pan theory and pg 2 for the Home Office and the Darling Family)
Specifically :
the idea that “Pan” is a title passed down. So there is not an actual Peter Pan, but rather a powerful fairy/shadow creature called the Pan who has magical powers. Whoever captures the shadow can use it for their own devices, controlling the shadow. Know what this sounds like? The dagger. Whoever has the dagger can use control the Dark One; whoever has the shadow controls it. If Bae eventually captures the shadow and controls it, at some point the implications that he has become like his father would hit. And maybe that is what caused him to leave NL and return to our world.
while I do think flying to NL is going to be the central way to get there, it doesn’t mean it’s the only way. They’ve hinted at “Neverland-adjacent” which is frustratingly opaque and could indicate that there are other ways to reach NL besides flying. And like I said, once George died, maybe the Home Office’s mission changed to eradicating magic (let’s go nuts and combine the two: maybe Dorothy took over the Home Office because she had been recruited by them when she got back from Oz and then she, years later, recruited GOAT). When companies change hands often times the mission and outlook of that company changes depending on who is now in charge.
And I do think it’s worth mentioning that the Home Office has probably been around for a long time, as they seem to have unparalleled resources at their disposal
In short, many of us have had the same thoughts so it sounds like a lot of us are really on to something here!