I do agree, solo budgies should never have mirrors (in fact, even budgies in a flock really shouldn't, either) as they contribute to antisocial and often, in extreme cases, aggressive behavior as they try to "defend" their friend in the mirror.
Spending time talking to him from outside his cage is good, and you can even put a perch outside his door so he has a fine place to sit when he does come out
Also, as he's settled in now, he's starting to consider his cage his "home" and sometimes may not want to come out. That's okay--you're doing a great job in understanding his needs and not forcing him
I'm glad he likes his healthy foods, even if you do have to hand feed them to him. My girl likes me to hand feed her veggies, too, better than eating the, by herself. She does like fresh, wet kale, romaine lettuce, or parsley hung from the top of her cage, though, maybe Comet will enjoy that?