Wow, they are pretty.
I've never tried asters from seed so, so I'm no help there. I also live in zone 6 so I really can't relate to gardening conditions in your climate if trying to germinate them outside. (By contrast to your 77°, it's 24° here. We had an ice storm overnight and our world, including my whole house, is covered with ice)
My only suggestion would be trying some commercial potting mix or seed starter mix, maybe they'd like the growing conditions better than straight peat. When you said your "covered lightly", did you mean with more peat or with plastic? Covering with plastic should help promote germination by retaining humidity. Clothier does say "germination slow" so if you hold on to that tray for a while some might sprout eventually.
I'm sorry that I don't have anything more helpful to add. Hopefully someone else will.
Karen
