A little bit should not harm your grass.
And, you are right, get your lawn to grow fast is the key.
I take it is raining a lot there? If not, watering less will help a lot. And when you water can make a big difference (early morning is best).
Ok, let's get creative ....
When considering how to deal with fungus, my mind often turns to something where there are limited amounts of parking spaces for fungi. What if a preferable form of fungi moved in and displaced the less preferable?
Take a look at
http://fungiperfecti.com/mycogrow/index.html for more info on some fungal stuff from fungi perfecti that is for creating a better turf.