Wondering how to stabilize

This is the basic mechanism how to hold the palette box attached to the tripod. As in the above photo, it's already firm against pushing down force at the front. However, it's still weak against down force on the side (photo below). At this moment I'm thinking two things:
1) raise the precision of the curvature.
2) add another layer above the current plate to have more than two points of contacts against the tripod.