2 ?s - zoysia and kids

Two questions - any help greatly appreciated.
My family began organic living (food, cleaning products, hygiene products, etc.) and now it's time for me to learn and implement organic lawncare. I have 2 kids under 4 with more to come. The boys are outside for 4 hours a day (mid-missouri). here are the questions:
1. our lawn is being invaded on 3 sides by zoysia - about 1/3 coverage - how should I treat it and do I plant new tall fescue in bare spots from last year's toxic applications and burning?

2. due to the intense outdoor play of Noble and Lincoln, should I plant or plug more zoysia or introduce more fescue or plant some clover/thyme? I need durability b/c the swing set is already down to the dirt in the first 2 weeks of decent weather.

thanks
Kevin

Whereabouts are you?  How cold does it get in the winter?

For me, I would be too lazy to try and get rid of another species of grass.  I might try to get rid of thistles because they impede my barefoot needs. 

Help me understand why you are thinking of getting rid of a species that seems to really thrive in your space.

Zoysia is tough stuff, impervious to almost everything. I'd let it grow. You won;t wear that stuff out