Do you have access to the attic space? This is often the easiest place to add insulation, and it can be just about anything that traps air. I'm right now in the process of putting just about anything up there...foam mattresses, styrofoam packing bits, bubble wrap and other clean plastic crumbled up, and cardboard. Yes it's all a rodent habitat but I've seen them nesting in pure fiberglass fluff too, so I just keep mousetraps set.
My house also has a crawl space, and it has mold and damp issues. Research has told me that attaching insulation directly to the wood under there will only make that problem worse. The only way to progress is to add the insulation to the foundation walls, preferably on the outside....this means digging a trench, etc. which is beyond my schedule these days. So we're doing rugs!
you've discovered the main advantage of wood stoves over fireplaces in heating efficiency. Wood stoves have better air control. One thing that would help would be to contrive a cold/outside air intake for the burn box of the fireplace...perhaps a hole through the floor? This might mean chipping or drilling through brick or cement, but it's worth considering. Then you can put glass doors in front of the fireplace and burn it as an enclosed chamber, like a wood stove. The goal is to heat up the thermal mass of the fireplace itself, which will then radiate warmth into the space. The better option, though pricey, is to add a stove that sits out in front of the fireplace, or even partly inside of it, that vents up the same chimney, or else somewhere else in the house. The issue to remember here is that for many people, firewood is nearly free, while other fuels aren't. Even an inefficient wood burning system is often better on the budget than the alternatives.