Well if you do manage to split them without damage, you might want to consider some additional tools. After just completing the headlight restoration on my new litronic lights I can tell you the pneumatic orbital sander is a must to remove significant amounts of material. You can puy the foam backed sander pads from mequires in 100 & 3000 grit from
Auto Detailing Solutions -- Meguiar's Car Wax, Auto Polish & Detailing Supplies Store that will do the job. If you have a harbor freight around you can get a Chicago orbital sander or other model plus a air compressor. But buy one larger than I did. The 3 gallon one is suitable for paint (what I really bought it for) but doesn't have a large enough capacity and compressor to keep up with the tool.
I wet sanded the exterior and did remove material. You'll need to do the same to get rid of the burn if it is just on the surface. Too deep and I think you can forget it.