Mr. Rogatinsky, a 49-year-old lawyer in Fort Lauderdale and a registered Democrat, said he was not motivated by politics, though he voted for Mr. Trump in 2016. He said his intent was to express “sincere appreciation” for the president’s attention to the broad swath of the Panhandle affected by the hurricane — and still awaiting the emergency relief funding that has been tied up in a political fight in Congress for seven months.

“The rally was so popular, and I saw that so many people were into it, so we said, ‘Let’s bring more attention to the area,’” Mr. Rogatinsky said. “It’s like the forgotten Panhandle.”

Two days after the president’s rally, Mr. Rogatinsky’s three stations — WASJ (adult contemporary), WKNK (country) and WRBA (classic rock) — began inserting snippets ranging from 90 seconds to two minutes of Mr. Trump’s rally speech into their hourly programming, without introduction or explanation and separate from commercial ads. Listeners phoned into the stations, mostly with words of praise, Mr. Rogatinsky said. He said his staff was searching for clips from other presidential speeches relevant to the region to feature in the future.

With 538 days until the election, and assuming the stations broadcast the bits of Mr. Trump’s speeches every hour, the time on the airwaves could amount to more than 25,000 minutes. That is equivalent to 430 hours, or nearly 18 days.

Not everyone shared Mr. Rogatinsky’s enthusiasm.

“I don’t think that him being on the radio for two minutes every hour is going to make an impact on the fact that we’ve had seven months of empty promises from him to help us here in the Panhandle,” said Winnie Byrd, the chairwoman of the Democratic Party in Bay County. “We still have people in tents, or in cars, living. We’ve got no federal aid.”