Personally, I say it makes no sense to have different versions of the same girl featured as different girls. So my proposal would be that there should be an option when a girl is selected to toggle between all available versions of her. Maybe where there are currently 4 circles that we can click on to select a pose:
1) Label that selection as "Pose" so it's clear what those circles are for. Possibly number the circles as well.
2) Add another line labeled as either "Costume" or "Set" with its own set of circles, or possibly icons representing the world or event that each set came from.
Some tweaks that might come with this change:
1) There would be one money collection button per girl, but its value would be calculated based on all the different versions of her that are unlocked.
2) Selecting a different costume/set could change a girl's type and stats. (Most recent event gave some different types from what they originally had. The devs would go back through and reassign previous event girls' types to fall in line with that new paradigm.) So each girl could have up to three separate stat distributions, one focused around each type. (This likely means changing up the favorite move for each costume as well.)
3) If/when there are different versions with the same type, multiple sets unlocked of the same type will multiply the girl's base stats for that type by a certain amount... Like maybe a 0.1% increase per each level of that version of the girl? Or however they want to do it.
For example, I have Noemy, Sporty Noemy, and Metal Noemy unlocked. If they made these changes there would only be one listing for Noemy in my harem but
1) she'd show some collection value worth around 3350 per hour (not exactly right, but that's close to the sum of the per hour values for those three costumes)
2) she might have charm stats when her normal form is selected, know-how stats when her sporty form is selected, or hardcore stats when her metal form is selected
Sorting options for the order of the harem list would be nice too, but it may not seem as important after de-cluttering the list by condensing the different costumes in this way.
Edit: By the way, I agree that the money collection animation was a strange addition the way they did it.