Yeah the tickets by themselves wont guarantee it but they open up to use pretty much anything else you have which is more than enough. Opportunity is half of the crime.
The LV increases whenever you have sex right? Then why not just have multiple sessions of sex in a single night and just focus on the sensei? She's smitten for all I know and you can just kindly ask her for a coochie without any dungeon item and she'll most likely want that too