I (and everyone) comes across Nanners from time to time.
What I’ve never come across is a nanner that pollinates a whole plant let alone a whole room.
They don’t produce pollen anywhere near the amount male flowers do, and what pollen they do produce is not very mobile. If they pollinate anything, it’s almost always the bud they’re growing from.
As long as you identify and remove them, you’re not going to get many seeds.
Like others have said, just ride it out and keep plucking.