I turned to Google looking for some assistance with this problem area and found that the answer appears to be no answer at all. All the sites recommend abandoning trying to plant in the area. Raised beds will be quickly infiltrated by the tree roots from below and digging out the roots harms the trees.
The best suggestion was using some form of above-ground planters. It seems silly to me to use containers in an area with plenty of soil, but I think this is my next step. I have an idea to build some low, rustic-style box planters to place in this area and see if the plants are any more successful.
I will keep you up to date on my progress.