Yes, there's "To Be Free," "Call Me a Princess," and "These Palace Walls."
The subtitle made me laugh though. "self-proclaimed 'members of the cult of Alan Menken'"
Plus, they are pretty respectful, like this quote:
JUSTIN PAUL We were incredibly nervous and intimidated to be adding something to what is such a glorious and iconic canon of songs. Of course, the advantage that we had — the only reason that we dared tread on that ground — is that we got to be in the room with Alan. Not only did he encourage us and allow us to find our own voice in this, he also shared with us. We got to see earlier drafts of some of the original songs in Aladdin, some of his and Howard's original work.
Although this line from Menken:
When we decided we were going to work together, they came over to my studio.
is definitely him being polite to both them and his bosses, because Disney decides those things and he has no control over it (for better or worse).
I agree with Menken that Jasmine is an unexplored character in the original film.