"One problem I have is that the open part of the thumbpick keeps getting caught in the strings"

Can you explain/describe this? I can't figure out what you mean. The thumbpick most generally only downstrokes. The open part is so far removed from the face (where the contact occurs) that I can't imagine how you're even digging in deep enough to have that kind of problem. Are you using one of those very short Kelly slick picks?