Edited my comment for more clarity. But the etymology of the spelling is all in the Wikipedia article if you'd just read that small 'spelling' section instead of stopping when you feel you've read something that backs your point. It was 100% driven by American marketers, not "Brits changing their minds", and yes 'Aluminium' most certainly had 'caught on in the US' and was the most popular spelling. Read Wikipedia - it cites sources in the form of several reputable books covering this history.

[..] in 1892, Hall used the Aluminum spelling in his advertising handbill for his new electrolytic method of producing the metal, despite his constant use of the Aluminium spelling in all the patents he filed between 1886 and 1903. It is unknown whether this spelling was introduced by mistake or intentionally, but Hall preferred aluminum since its introduction because it resembled platinum, the name of a prestigious metal.[141] By 1890, both spellings had been common in the United States, the -ium spelling being slightly more common; by 1895, the situation had reversed; by 1900, aluminum had become twice as common as aluminium; in the next decade, the -um spelling dominated American usage. In 1925, the American Chemical Society adopted this spelling.[135]