Government of Time: Weren't you supposed to go to the Taisho era to deal with the historical revisionists? How did you lose my very own Master?
Former savior, current missing Master, Gudako lost her memory in an accident and somehow ended up cooking for the Demon Slayer Corps?
Emiya: How are you all still alive with the way your Master cooks?
A certain attendant: I've never even eaten a meal made by my lord!
Gudako: My cooking may be awful, but I'm great at ripping demons apart with my bare hands! I just don't know why these things don't drop materials! [Demon: ???]
FGO + Touken Ranbu + Demon Slayer
Don't ask. The answer is always that she tears Muzan apart with her bare hands.
Warning: actual bare-handed demon-splitting ahead. A chaotic evil doesn't need a Breathing Style to pin a demon down and beat it to a pulp.
As for the CP, maybe in a bonus chapter. All the swords and Servants are in love with Gudako.
Theme: Hey, buddy, you know what they say: what goes around comes around.