I'm the original poster. I found an obscure reference, after many Google probes, to a method called GeometryRequest. I don't know why the following is even necessary, but it works:

$ScrolledCanvas->configure(-height => $Ht);
$ScrolledCanvas->GeometryRequest($ScrolledCanvas->cget(-width), $Ht);
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Knowing only that it works leaves me a bit cold. It looks like brute force in the face of failed finesse, but if someone can explain why it's necessary, I'd be most grateful!

Many thanks.