How do I replace Essentials stuff with my own?

Ok, maybe I simply am bad at this, but no matter what I do, when I start a new game and try to transfer over the data/audio/etc files, it just turns into the Pokemon Essentials game. (Granted, all my experience is in VXAce, I've never used XP, so I might just have no idea what I'm doing...) How can I create my own game, using the kit Essentials provides, instead of creating "Essentials, the edited version"?

Just add your own maps to "Essentials: the edited version".

Pokémon Essentials is not a magical program. It is an RMXP game, no more and no less. It contains assets (graphics/audio/scripts/other data) that make this RMXP game look and behave like a Pokémon game. What makes it a starter kit is that it (the RMXP game project) hasn't been completed, and it is distributed in project form so that other people can modify it however they like. I don't particularly like the term "starter kit" for this reason - it implies there are tools and things beyond just an RMXP project, which there aren't.

As mentioned, your task is to edit what the Essentials RMXP project comes with, by adding your own maps and characters and such, to make it look how you want. You can delete the maps that come with Essentials if you want, and start making maps from scratch, but those maps have lots of examples of things and are very useful. In any case, you should treat a freshly downloaded version of Essentials as your very first game project backup.