Since these plants are not breaking the bottom of the plastic pots, but rather getting through the drain holes, I believe some plastic would prevent the downward growth and force the root growth sideways.
Anything that will stop water will usually also stop roots.
Plastic sheeting will work, at least for a couple of years. I have seen roots punch holes through it, but it usually takes time for something like that to happen.
A wide hard tile of some sort is ideal, maybe even a paving stone of some sort. I have seen people use wood, but it will rot away after a few seasons years, and may not last longer than a year in some climates. It's more practical in dry climates.
Depending on the tree species, and your soil and climate, place the tile or plastic about one to two hand widths below the soil, and place the tree directly on top. Arrange the roots to spread outward, and fill in the hole. Remember that planting shallower may require you water more frequently, at least until the roots reach the edges of the tile/plastic and start heading downward.
You can got out once or twice a year and dig around the perimeter of the tile to sever roots that are growing out past it. This will encourage more roots in the top of the tile, but again, you will likely have to water and fertilize more.