Am I right in imagining that the high cold water flow is pulling hot water out of the hot lines? Is it safe to put a flapper check valve into the 3/4" cold feed before the water heater? Thanks.
Can''t happen. To do so would require having a suction in the hot lines and a vent to allow air to enter as the water is sucked out. Neither of which can happen in a water system in the USA. You either have an inaccurate perception or something else is occuring.