how to out-compete grass? - New Orleans suburb

Hi all
i am in the New Orleans area, in a suburban setting and am turning my backyard into a food-forest.
i am growing a lot of fruit trees, as well as herbs etc...

My biggest problem is grass.
I have used cardboard and newspaper, which works, but, its a lot of work, and breaks down eventually.
i need some suggestions for plants that will outcompete the grass...
OR? other suggestions ?

i need it for shade areas, and also full sun

Here is a quick list of what i am growing...
loquat, blackberry, passionflower, basil, starfruit, jujube, banana, guava, papaya, mango, several citrus.

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Sweet potato makes a dense groundcover that will even outcompete Bermuda grass and will be a perennial plant in your climate.