Could disconnect the hoses to the core. Plug or connect to each other temporarily and attach some extra hose to the core connections. Take one gallon of water and mix with bottle of Preston flush. It should come out really concentrated that way. Pour the mixture down one hose until it comes out the other. May be let it sit for 1/2 hour since it is not circulating and afterwards use a hoe or something with low pressure, flush it out in the opposite direction. Which I believe you would want the water pressure on the connection that did not have the water valve on it. If correct that would back flush it. Run it clear and if possible use some low pressure air to push the remaining liquid out. Then reconnect, bleed out any air by one or two cycles of engine hot/cold and watch the reservoir to ensure it does not go down to much when cold as to suck in air again. The only reason I mentioned the air blowing is so you don't dilute your coolant mixture down any more when hooked up with water but you can always add more coolant concentrate like when topping of during the bleeding process process perhaps. I don't think the concentrated cleaner will do any harm by sitting in your core for a little while. If it leaks later corrosion is probably what was holding it together. Till it was flushed out.