Okay, I've gathered my thoughts, and this is where I'm at:
+We have 45x20' to work with
+It was probably over-worked in the past. Was lighter in color than the rest of our lawn, and only covered in weeds (no grass to speak of)
+We have a lot of wood chips, and some cardboard, covering this area. I have a pile of wood chips left, and also a compost bin that I built, and have some compost cooking in (not ready to spread)
+We need to re-lay some of the cardboard, as I skimped in certain areas, and have serious crab grass growing
+I roast my own coffee, and can cheaply grind and brew leftovers to add to compost/garden
We really, really want simple. I am an engineer, and understand the benefits of nuance, but getting too much in the weeds (no pun intended) is a tendency of mine. I need to focus on simplicity, and the big picture. I really just want someone to tell me that I can mix a bunch of compost into my wood chip-covered garden and all will be well. Or, if that will deplete nitrogen too much (as wood chips decompose), maybe I just need to lay down more compost (while pulling back the wood chips, and cutting through the cardboard), and use the same method I did initially. Are wood chips part of the issue? Should I remove them? Should I just purchase a bunch of compost to get started? I really do appreciate all of the posts thus far, and am confident this can be a success!