In theory, we could dilate time around Janepoints such that Jane synced her point to - Bell Standard Time, let's go with that - and the rest of the world followed along at a fraction of that rate, but we don't actually know how Jane's time syncing works, and if it breaks we have bigger problems than a few months going by in worlds we haven't begun to handle yet. This also wouldn't let Jane use the Internets on worlds that have them, though that's a relatively more minor concern.

People seem to have inflated ideas about what my aura can do. I can get a door from a world to Milliways whenever I want. I can get Milliways to let me door out to any world I've been to before without spending a coin to force it. And I can sometimes get a door to a world I haven't visited before, but I need something to go on. I didn't get a door to Materia. I did get a door to Rainbow, but only when I had someone on hand who had met someone from Rainbow. I can't just door to unspecified Janeless worlds.