"To beat the band" means "to outdo one's rivals".
Imagine a brass band: you would have to sing or play very loudly to be heard above their noise.
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Most of the whisky professionals I asked assured me that there was no such thing as innovation at their tradition-steeped distillery -- they were doing everything the same way it had been done for generations, thank you very much. Some distillers seemed put out that their companies had recently embraced such cutting-edge twentieth-century technology as labelling barrels with bar codes. The marketing side of the business is innovating to beat the band -- look for a new Irish whiskey called Feckin and a new rye called (rī)1 coming soon to bars near you -- but the production side remains defiantly old-fangled.
Cheating the Angels | Popular Science
I have no idea what beat the band means
My dictionary of English slang says "to beat the band" means "strongly" or "to an extreme degree".
It was raining "to beat the band" (It was raining "strongly").
He drank "to beat the band" (he was drank "to an extreme degree").
Hope it helps