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Ok, then snow loads on the patio roof are not an issue. While what you describe didn't go right the first time, the proposed fix should be an acceptable solution but I'd ask for a minimum 3" pour on top since it sounds like the original pour was not as thick as it should have been.
If the pour is at least 3" it's virtually the same as an independent pour. I'd want them to use re-wire in the pour or at least polypro fibers in the mix (polypropylene fibers that inhibit cracking). A 1" drop over 8' is ok ut there's no reason they can't maintain more pitch. Water penetration is not an issue unless the slab cracks