You can try some Prestone radiator flush in the cooling system before you start flushing the core; It might be enough to loosen the crud in there. When you backflush, be very careful about using too much water pressure. It's very tempting to try to "blast" out the debris, but it could lead to tragic results (don't ask)....Good luck and post back your results.

You can disconnect the heater hoses in the engine bay where they connect to the stubs on the bulkhead near the brake servo. The hose that connects to the cylinder head is the input to the heater, so to backflush, you inject into the other (outlet) one. I connected lengths of heater hose to the stubs and used a funnel to pour that CLR household scale remover in and fill the core. Then lower one hose into a container and drain the core, capturing the CLR.

Vinegar (a weak acetic acid) will also work, and if you can get some horticultural vinegar at the garden supply store, that is a much stronger acid.

Connect a garden hose to the outlet and backflush. Go easy on the rate/pressure! Typical house water supply can be 5-to-7 times the pressure the car's system is designed for. On my son's 81, I repeated this CLR&flush cycle many times until the bits of tan-coloured deposits and scale stopped coming out.

This gave us a huge improvement in heater performance, but there is a possibility that the scale in there is plugging leaks, so try this at your own risk.