Hi Jethro, just caught up with this thread, looks like you may have been using an orbital sander to sand through such a large area.
Where about's on the body is the damage ? If its on the bottom edge a trapeze bridge hinge could possibly hide this.
It will be hard to repair with a veneer that will match.
If it can't be hidden then I think your plan sounds the best. Choose a dark timbermate colour and you may be able to stain the burst. Otherwise paint the burst edges and green stain on the inside of the burst.
We've seen this problem happen quite often. Could be good to put a warning in capped kits for new builders that the caps are very thin and easy to sand through