That should work for you. Distilled water and one of those bottles and see how it works. Be interesting to see what you find when you pull the thermostat. Did you check to see if your thermostat seems to be working properly now? Top hose should be cool until the thermostat opens and there shouldn't be flow in the radiator. So fairly easy test to run.
No signs of coolant flow looking in the top of the radiator on a cold start . Ive ordered a couple different thermostats to test out, in both temp ranges and style .
