I think I've finally figured out how to "complete" Gustave quest. I'm using quotation marks because I'm not sure if this is the actual ending, but it’s the furthest I’ve reached so far. I will update this if I find anything new.
Before you do anything:
- Completing this quest has annoying side effect (I still don't know if they are permanent or not): you will lose access to the Senate and the Academy (including the statue at the Academy).
- I strongly recommend that you never talk to Regulus, just to be safe (aside from the initial interaction when he drops the letter), and do not give him the letter back. This quest is extremely buggy at the moment; interacting with either of them may break it at some point.
- You will need to have Negotiation at 50. (or Sex Appeal at 60, this might work but I didn't try).
Guide:
1. Ignore Regulus (you may pick up the letter) and go talk to Gustave. Choose the option "Support Gustave".
2. Go to the prison and make a visit, go talk to the guy in the bottom-left cell. Give him the "Unsealed Wine", then return to Gustave.
3. Return to Gustave in the next, he will give you a list.
4. Find the three people on the list: 1 - First one, in the Metal Shop (Upper Residential District); 2 - Second one, in the Sauna (+ blowjob scene if you choose the "Flower Seller" option) and 3 - Third one, in the Casino VIP area, the guy at the middle slot machine.
4.1 The third one is the one you want to kill. You have two ways: 1 - give him the "Unsealed Wine" or 2 - use Negotiate (requires 50 Negotiation) twice over two different days, then choose "Purge Him" option (he will ignore you on "Flower Seller" and "Plunder" options).
5. Go back to Gustave the next day to receive the "Banquet Invitation".
5.1. If you dont have the mask or dress, you can buy them at the shop next to the Metal Shop in the Upper Residential District.
6. At the banquet, talk to Knight Bernhardt (top-right seat), use Negotiate (Negotiation 50, I recommend this option) or Flower Selling (Sex Appeal 60) and choose "An empty illusion" to gain his trust (Yes, you need to talk to him, there's no other way to continue the quest). When the time comes to exchange gifts, give Bernhardt the "Unsealed Wine".
7. Return to Gustave. You can choose one of three rewards: 1 - "I want money": 5500G; 2 - "I want fame": 100 fame or 3 - "I want to get my memories back": 4 Impure Seeds.
7.1 All options will lead to a similar h-scene with Gustave at the Academy statue, with variations in dialogue.
And that's it for now. I still don't know if the Senate or the Academy will reopen, but skipping a few days doesn't change anything.
BTW I only managed to complete this quest in my NG+ because the requirement for Bernhardt was very high (trying to change my build at that point would require a lot of farming), and again, this quest is annoying to complete because you can easily break it if you don't do everything right (like on my first run, Bernhardt didn't show up at the banquet and I couldn't do anything about it, I have no idea why).