Before quest we have 2 choice groups, Steampunk/Goth and Punk/Raver.
What make decisions confusing is there are 2 overall goals, one for the trash quest, the other for the rocketship. There are 4 different ways to complete the trash quest.
1: Have a mohawk wig (from the airship) equipped and go fight a Punk Rock Giant (676/4 => 678/1). Issue with this is you must have the wig equipped before the choice adventure.
2: Have a model airship (from the airship) and go pick a fight with the Steampunk Giant (675/4 => 677/1). Usually easier because you just need it in your inventory. Not guaranteed.
3: Swipe a record (678/4 => 676/2) then play it for the Goth Giant (677/4 => 675/2). Always available but requires NCs to happen in a certain order.
4: Mousehole. Nobody wants this.
1 and 2 both have a 50/50 chance of getting the needed NC, then your quest is done and the next NC can take you to the rocketship thanks to the Punk Rock Giant flinging his trash can. With 1, if you get the Steampunk option first, you can grabs the rocketship and try again. No major loss, plus this allows you to skip the steampunk in the future.
3 takes a twist. I've looked at it several ways, and if you must take this route, you need to get 2 choice groups back to back, Raver record then Goth giant. You have a 25% chance of getting these in the order you need them. If you get the Steampunk chance first, though, you can get the rocketship and not lose out on a turn, similar to 1. If you get the Raver option after getting the record, you can skip it in the future.
Perhaps an option can be made to intelligently complete this quest, depending on gear and inventory, letting mafia pick the best option available from the choices. The difficult part comes in if you don't have a mohawk equipped but have a model airship. The only way to skip the Punk/Raver is to grab the Raver's record so you can skip it in the future. Only helpful if you get another P/R choice.
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After the quest is done and you have the rocket ship, there are 2 sets of real choices that can be made.
Set one, fight the Steampunk or Goth Giant, farm brass gears or thin black candles, or skip the adventure.
Set two, fight the Punk Rock or Raver Giant, farm money, heal HP & MP, or go to the Steampunk's room, which then automates based on their preference.
After quest, this is looking similar to the Louvre choice settings except you don't need to figure out what goes where.
**I know the rocketship is technically optional if you pull 2-4 star key lime pies and a star chart, star hat, and star weapon.