My newly acquired boat came with a MD7A that is not pumping water. I plan to try and flush the system using a trick I saw in an old magazine. The article described attaching a bilge pump to the water intake hose and sticking in a bucket. The water output was routed via a hose back to the bucket. This way a cleaning solution of some sort (water and vinegar maybe?) could be continually cycled through. I replaced the water intake ball valve with a safety seacock. So it will should be easy for me to switch off the outside water and redirect water intake from a bucket.
This is, of course, after I check simple things like replacing the impeller. You might try the bilge pump trick to force any air out of your system (assuming this is even an issue).
I was thinking of using a 50%/50% vinegar/water solution and circulate as you state through my direct sea water cooled yanmar. Maybe do this once a year. Do you think this would clean the deposits off the internals of engine? I am a little hesitant about using any stronger chemical as it might damage the engine metals.