re: I suck at Google: who should I call to repour my back porch/patio?

Would not recommend. It will begin to de-laminate within two years, probably sooner. Using concrete, you need a depth of twice whatever nominal sized aggregate you are using.

#7 stone is 1" nominal so you would need a minimum of 2"

#57 is 1 1/2" so you need 3"

I would recommend you demo the old slab and replace the whole thing.