You can build the area up - no soil against the tree trunks and I hope you caught Chapter 5 of our Earthwise Soil Prep webinar for the explanation of determining how much of the tree's root zone you will be affecting. If you add soil over an area that's 1/3 or less of the tree's root zone and you guard the other 2/3 from damage you can transform a garden. But you might have unrealistic expectations of the area. With large trees overhead your garden has to be considered the junior partner. That is, plant with the expectation that your garden will NOT be lush and jam packed. But that doesn't mean it must look thin and poor. Choose your places under the trees to add up to maybe 40% of the space and plant that 40% heavily and with impact. Maybe one central spot has a mass of Japanese painted fern -- good in dryish areas and in some varieties so gray-white in leaf color it looks from a distance like a spotlight in a shady area. And places to right and left of the fern have huge leaf yellow-and-green variegated hostas. Between planted spots leave graceful space in curving-edged chunks or in actual paths with benches or wood sculptures along the way.
I hope this helps!