I wouldn't flush the core if it has flow. That might remove some deposits, but at the same time it uncovers areas for new corrosion to start. Copper and aluminum benefit from having scale or oxidation layers to prevent further corrosion.
I still think you're gambling here and would replace the core of your 23-year-old. OTOH, I guess you don't need heat that often in SoCal. If it does leak, seal it off and wear a jacket.

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Prost!