"Прекрасно" is "good in every way", "perfect", it is something that cause wonder and delight or feeling of exaltation. So it's not about beauty. It's about what beauty of something do to you.
I would say that "прекрасно" is "harmonious and so beautiful" in this context.
¹ Moreover, nobody ever translated the name of the Russian fairy tale Василиса Прекрасная as Vasilisa the Excellent.
I think "beautiful" is more subtle (less banal, if you will) than "красивый". And so is "прекрасный".
I agree, but I'd say "excellent" is even further away in meaning. Translating between such distant languages is always an exercise in compromise, unless you're willing to take great liberties at interpretation (when translating poetry, for example).
Excellent is closer to идеально. Both imply relative comparison (to others). Beautiful is an absolute characteristic, same as красиво, so it's a better fit here.
Probably nitpicking, but I'd translate "прекрасно" as "beautiful" here.