I've been digging in the code a bit, and found a way to make the thumbnails into squares:
kpg.class.php, line 216:
change
$url = 'http://picasaweb.google.com/data/feed/api/user/'.urlencode($this->username).'/album/'.urlencode($album).'?kind=photo';
into
$url = 'http://picasaweb.google.com/data/feed/api/user/'.urlencode($this->username).'/album/'.urlencode($album).'?kind=photo&thumbsize=144c';'
(add &thumbsize=xxxc - the c stands for 'cropped'
kpg.class.php, line 329-331:
change
$thumbURL = (string) $photo->media_group->media_thumbnail[1]['url'];
$thumbW = (string) $photo->media_group->media_thumbnail[1]['width'];
$thumbH = (string) $photo->media_group->media_thumbnail[1]['height'];
into
$thumbURL = (string) $photo->media_group->media_thumbnail[0]['url'];
$thumbW = (string) $photo->media_group->media_thumbnail[0]['width'];
$thumbH = (string) $photo->media_group->media_thumbnail[0]['height'];
This solution is of course a bit messy - the thumbnail size is now hard-coded in the php file.
But it works like a charm...