When surrounded by trees..any kind, my yard Pine and Cottonwood and Aspen..and green ash..most all of the trees are right on the fence line of my residence. The shade is, was, not my problem the problem is..the roots SUCKS the life out of the soil.. so.. I grow in old horse toughs, cattle lick pots,.. All with 1/2 drain holes..and on cement pavers.. the pavers.. is a must because the roots..WILL go right up into the containers..just weed barrier will NOT be enough.. and I grow plenty!
Invasive plants are Earth's way of insisting we notice her medicines. Stephen Herrod Buhner
Everyone learns what works by learning what doesn't work. Stephen Herrod Buhner
They do all sound like trees with spreading surface roots....isn't an aspen one of the worlds largest living organisms? I suppose you could try putting some of the paving slabs vertically to make a barrier, cutting though the roots. It does sound like trying to grow vegetables there is working against nature rather than with it. I wonder how else to tip the balance....Probably with perennials and shrubs that cover the ground and can get their roots past the tree roots and deep, rather than annual vegetables.
I'm a big fan of creating raised beds on top of poor soils in able to grow things on them.
They do not need boundaries or walls if you do not want them (like a raised wooden garden bed) but it can rather be a mound of material on top of a spot. I usually use a smother layer to take care of weeds, a few inches of thick well produced compost and then some mulch on top.
As you grow in them, you can keep an eye out for root intrusion but I think you will have plenty of years of success.
It sounds like you have a different take on the forest gardening problem, one that works.
Are you tired of the need to garden in containers?
I happen to have two mulberry trees next to my very large chicken composting yard and they grow a network of roots deep into the pile.
I accept it as gift , because they don't seem to sprout from the root fragments and living roots feed soil organisms.
I will be trying to establish elderberry along the edges of that pile, for their alleged compost accelerating properties.
I most falls I create compost bins out of pallet wood, often right under the fruit trees I favor.
I fill the bottom with woody biomass, followed by leaves and urine.
I plant tomatoes and squash transplants into the unfinished compost, water and walk away.
Later I harvest what's there, and add a deep layer of leaves/urine.
I repeat this cycle until the pallets start to rot ,then I harvest the compost, taking whatever isn't fully decayed and adding it the bottom of a new compost bin/ garden bed.
The tree roots tend to stay in the soil proper, probably because so many nutrients are leach into it from above.
This method or some variation might free you from the need for actual containers, though I've found these beds are good places to put containers of seedlings, to keep them from drying out.
I've recently built a table style bed at my mother's house.
The top of the soil is about 30" off the ground.
It has already produced a flush of turnip greens, from transplants that had been languishing in a ground level bed.