Kristi, I put my very tiny basil in a mini-greenhouse inside my greenhouse because we were still having cold nights. BUT, you HAVE to open it up on sunny days. Good idea to open every day for circulation anyway. I haven't tried anything more tender, but you're in the same zone I am so you could try. Not to germinate, but after potting up.
I have taken the covers off completely now even though we are expected to get low 30s again Wed. night. And I have one pepper that got put out by mistake with no added protection and it's fine.
Maybe try a couple plants so you don't lose everything!
