I now see that's the best way to create new documents in the future... I was even thinking of creating separate backing styles (each based on Normal) for every heading altogether. And let the "Heading" style just be a front. More work, but easier to mix it up later.

But for the existing document, this isn't a solution. If I change the "Based on" now, the appearance of the style changes (which isn't illogical of course).