Following on from the above, if I set the Autonav “Automatic image sizing” parameters to 150×150 (i.e. the same as my default WordPress thumbnail size, specified in Settings, Media), Autonav displays consistent square thumbnails for every image, as expected.
I’ve checked out the plugin code and, while I’m no programmer, I can see that this is consistent with the way the plugin works – it looks for the correct size of image first (as defined by filename) before creating one itself. These images already exist.
Still trying to work out why it isn’t creating the cropped images when they don’t exist. Not simply failing to creating them (which could be a permissions issue), but creating scaled images instead.