Another option (if you are within a certain range of the NWS alert transmitter), is to purchase a used "fire department" pager and have the NWS frequency and alert tone programmed into it. Some models even have a voice feature that plays the warning information over the internal speaker or saves it until you activate it. Minitor is the model that comes to mind, though there are others. That would take care of your delay problem, as the warning comes straight from the NWS and doesn't have to pass through a paging service, TV or radio station.
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AJ