I would be inclined to tackle this problem 'starting from scratch' rather than trying to make sense of existing ways to sort/choose fonts. So principle component analysis might be one way to go, maybe identifying new 'principle components' to better sort/arrange fonts by.

I also wonder if the work done in OCR could be useful. To be able to recognise a font takes you half way there to categorising a font.

Another thing with font choosers is that sometimes you need a font sympathetic with existing material, perhaps a licensed font that you just don't want to run on a website. Maybe that font has an opentail 'g' and you really need to restrict your choice to fonts with an opentail 'g'. Or you find your best match font and then a little while later find that it has the wrong style of 'a' that you ended up with. There is no easy way other than typing in a better 'Quick brown fox...' and sifting through previews, ideally you would want to refine by things like opentail 'g' - something a layman can understand and not a typo term.