Hi @dan-mnation,
I always have to check this so forgive me if it's rudimentary, but when you refer to penetrations are you actually talking about penetrations or intersections? Penetrations are when the thickness or shell parts overlap a mesh, while intersections occur when a node of a mesh intersects an element of another part in that contact. Intersections can seriously effect your simulation and should always be removed, while penetrations are less severe and don't need to be removed entirely but can still affect your simulation.
I'll assume that you are talking about penetrations. You can get nonphysical response from these due to LS-Dyna attempting to correct for them at the start of the simulation. So the nodes will be adjusted to remove these penetrations and will deform the mesh. You turn this off for individual contacts within each *Contact or for all contacts in *Control_contact by setting IGNORE=1 or 2. With this option, the shell thickness will be reduced to account for penetrations instead of manipulating the mesh. This may help reduce some of these pressure concentrations.