when you use that LM radiator cleaner be sure that NO COOLANT is in the engine. drain and collect all of it for reuse.
The thermostat valve needs to be taken out and air used to push all coolant out of the block too, then put everything back without thermostat valve, fill with clean water and LM cleaner and start engine, drive around for 20 minutes or less, come back, open hood, spray radiator core with cold water, remove radiator cap and shut down engine, drain slowly from radiator petcock with low pressure water hose in the radiator neck, the clean water will slowly get mixed with the dirty and hot water and flush out, it will take about 30 minutes. Once you are done, remove Tstat valve elbow and use a blower to push out all water that is trapped in the block - put everything back along with Tstat valve, fill with your collected coolant or new coolant and you are good to go.
The reason your car needs air for water to be pushed out is because it does not have a block drain like most sensible engines have.