Gary Seitz (and various collaborators over the years) have worked out lots of concrete information about maximal closed subgroups of classical groups and exceptional algebraic groups over an algebraically closed field of prime characteristic. Much of this is used in the study of maximal subgroups of corresponding finite groups of Lie type. Anyway, a basic 1987 paper on classical algebraic groups by Seitz is here.
I don't have all this information at my fingertips, but I suspect you can already draw a complete answer to your question from this substantial paper. He imitates some of the methods used by Dynkin in characteristic 0, though his results are more subtle. (If I have time today, I'll try to comment further on your special cases after refreshing my knowledge of what Seitz found. He is formally retired at U. Oregon, but could perhaps pinpoint exact results if asked by email.)