I'm thinking in Lousiana, the mottled/dappled shade might be to your advantage and allow you to keep growing some things that would normally shut down or even go down from the heat during the summer.
With the huge leathery leaves, I think the problem might arise when the magnolia begins to drop leaves. Are they one of the earlier trees to drop leaves in the fall or do they persist until later? ...or -- huh it just occurred to me -- are they evergreen in Louisiana?
If so, then I think you are more likely to have problems in the fall and winter garden when the sun is less intense.
This is exactly the kind of "micro-climate" that can only be explored by experimentation. Try growing different things and take plenty of notes. (And let us know! Other gardeners in similar climate may have similar results
) I wonder if you may have more problems due to the magnolia stealing all the moisture from the ground....?