Welcome, Gavin. You've come to the right place.
In addition to masonry heaters, you might want to check out
Rocket Mass Heaters (RMHs for short), of which there is quite a lot of information on this site.
But in general, yes, using what you already have until such time as its useful life ends is most cost-effective, and most respectful of the unit's embodied energy costs. The only other factor that way is the cost of fuel, both financial and environmental.
Were it possible to build a small
RMH, you might find yourself heating with twigs and branches gathered from the ground and using your existing system only for base heat and
hot water. This, I think, would be a good way to slowly transition towards a better heating solution without ripping out perfectly functional infrastructure, and saving money on fuel at the same time.
But let us know what you decide, and good luck.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein