Another way is looking at installing an inline extractor fan, I know you have a fan installed but if you have space above in the void/loft these are three times the power of a wall mounted bathroom axial fan. As they are installed outside the room they are just as quiet too.
Vortice Inline Duct Fan is an extremely powerful bathroom extractor fan which is energy efficient and very quiet. Very powerful and very quiet.
extractorfans.shop
This will extract a lot of air at a similar energy usage rate of a bathroom fan.