So, I tried again and it was really, really close! DF liked it so much, that we ended up ordering pizza last night, because I was intending on serving the leftovers, but they magically disappeared at lunch time!
I doubled the paprika, increased the flour by 1.5 times (the last batch was too thin), and only used chicken thighs (which is all I've ever been served at the restaurant). Something I forgot to mention in the OP, I used an immersion blender after adding the first cup of water. The sauce is supposed to be uniformly orange, Mama must have some mad knife skills to chop the veggies fine enough to create that without one!
It's still a little off, which I think may be the fault of the sour cream. At the restaurant, they serve cucumber salad with sour cream on it, and it tastes quite different from "normal" sour cream that you buy at the grocery store. I assume that they use the same stuff in the paprikas, but haven't a clue where to find it. I know that you can make sour cream, but wouldn't know which method/ingredients to use to yield their result. Any secret knowledge about sour cream? Are there specialty stores that have it fresh?