There's a more going on than just fermentables for rum production. Are you using nutrients? Monitoring and adjusting your pH? What sort of numbers were you getting for gravities and yield?
Solids are particles in suspension - sugars, acids, minerals, protein, fats, etc. I found a paper from the 40's on the breakdown in molasses. Ash would be the solids that don't burn off. The data sheet the molasses supplier gave you is as good as you'll get without some heavy lab equipment, but you can run a test fermentation under ideal conditions to determine expected yield.