Phosphoric and citric acids work very well on calcium deposits, and are not as nasty as (for instance) hydrochloric acid, both for one’s health (breathing or skin) and for the metal itself. Phosphoric acid is used as a industrial cleaner for copper and brass, as well as a rust-cleaning agent in retail/diy formulas. Cleaning a cooling circuit with either should not generate any kind of corrosion issues. Citric acid is easy and cheap to find (at least in Europe), it is one of the base products in any good housekeeping cupboard, together with baking soda, ammonia, etc. Phosphoric acid is a bit less common, but you can find it in large DIY stores. Fill the circuit with clear water, add citric or phosphoric acid, run the engine until hot, let it rest a little (1/2/3 hours depending on how dirty it is), flush/rinse with clear water until the water runs clean. Fill with appropriate cooling fluid. I’ve done this with each and every one of the old engines I ended up having throughout my life (not my Pagoda as the engine had been completely redone -and the radiator too- just before I bought it), never had any issue, and never had any cooling issues thereafter.