I'm intrigued by the use of level set domains here. I've only encountered those in other type of numerical simulation where the intent is in avoiding surface meshing.
I suppose moving an object in this context is as simple as composing its level set function with a translation and rotation. However, deforming is non trivial, especially local deformations, right?
How do you efficiently resolve collisions? At the scale of an element, it seems to be a simple check of nowhere should both level set functions be negative. But how do you select the elements to check? Do you somehow keep track of only the elements traversed by the objects in a time step, or some other method? I would guess your method should be more efficient than intersecting meshes, is that what you've found?
I'm particularly interested by your mention of high-order boundary parameterizations, what do you mean by that exactly?
Sorry to bombard you with questions, I was intrigued by a combination of things I'd never seen together before!