Unless I'm understanding you wrong, literally everything you have described here is already how the editor works; except that the details for each individual folder of styles are listed in a "style.ini" folder in the subdirectories rather than the main "NeoLemmixStyles.ini" folder.
(For the record, you can use negative numbers for the ordering if, for any reason, you want to put styles at the start of the ordering.)
The ordering of the default ones (eg. Sega being after the LPII / LPIII styles) is a carry-over from when they were done by number. You can change their order, but just be aware that older levels (as in, very very old - 2KB or early 10KB levels; or vanilla Lemmix levels loaded directly into NeoLemmix style) may initially load in the wrong style; of course, they'll be fine if you manually change them to the correct one.