figmus, it sounds like ur situation is very similar to mine, except that i'm hoping to be out on the property this spring. i wouldn't say my soil is poor, lots of grass where the cedars aren't, but it IS rocky and presumeably acid.
what i've done is cut the trees from the entire garden area (almost exclusively cedar, some sumac), laid the trunks aside for later use, and burned the remainder. i open a single bed at a time; mine are usually about 4X8 or 4X12. it varies cuz of the stumps. i plan to get rid of them some other time.
then i spread ashes and lime on the worked bed but of course don't have enough ash for the whole garden area. i have brush piles to burn elsewhere of course.
the ashes are high in phosphorous and potassium. i'd prefer to spread the ash later when the soil is warm, cuz the soil microorganisms pick up some of the nutrients and hold them till they die, which is better than letting it all leach away.
i plan to grow some green manure crops in some of the beds, but i am anxious to get a crop too. i ain't got a pick up truck yet so can't haul too much manure. probably use some sawdust to loosen the soil and add organic matter. then dig in some manure (bought by the bag which i hate) or maybe cottonseed meal. or maybe some alfalfa, which has almost as much nitrogen as manure, and is at least a bit nicer to haul in a car. and a LOT easire to carry on the roof!
not all veggies need sunlight all day. some will tolerate some shade, esp. in warmer weather. the more sun the better of course, but i don't like killing trees. also if u surround ur garden area with flower plantings (which is said to attract beneficial insects and is just plain purty) the somewhat shaded area won't hurt them a bit.
i'd like to know more about what ur doing.