Sorry to hear it bagginsbill.

The only solution I could see would be to rebuild the entire lid in a Modeler as a manifold/closed object with control loops to facilitate the hard edges and sufficient poly count to allow the modeled engraving (how I interprate your description). I'm familiar with manifold or closed volume modeling simply because that's how Wings3D does things, my preferred Modeler.

Obviously the above isn't remotely a realistic option, nor is purchasing a modeler for a single function that may or may not work in this instance (although downloading the trial of Silo and checking out Unify Normals is a thought).

I wonder what application the model was built in/intended for?