At the moment I'm sitting here looking for a mate for one of my Sylesti(s?). I keep finding ones that would be great, they have a breeding cost, I go to breed and... they are unconscious. I understand I can opt to pay 250g to feed their pet to breed, which I don't mind for some of the ones that have a minimal breeding fee. But for some of the higher ones, it would be nice to filter by consciousness, or add to the statistics section on the search that they are unconscious, to save some time.

While I agree it would be nice to filter by consciousness (mainly because its pretty inconvenient!), I just wanted to double-check that you're aware that you can revive unconscious pets?
If you find an unconscious pet there will be a "Feed Sylesti" button which you can click on, spend 250g and it'll revive them. In the scheme of some of the higher breeding fees, an additional 250g is nothing.
:)

Yup, I did point that out, though to be honest until I decided to click that button, I didn't know that was what it would do, so I passed up quite a few Sylesti partners until I decided to take that step, since nothing really indicated that to feed one would make it available. Maybe just editing the pop up (I didn't realize a couple were unconscious) to say "Error: Sylesti is unconscious. You can feed it if you want to breed!" might even work.