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You might try The Brothers Grimm Spectaculathon for the one-act. There are a lot of fun parts in general but the Cinderella scene sounds like it might be perfect for your kid. One actor ends up playing almost every part in the story (including the birds). 

Another option for the one-act is 11 Variations of Friar John's Failure. Again, lots of good characters in general but very definitely a lead comic male is needed to keep it together.   

For your musical something like Kiss Me, Kate might be a good option. 

It might be a bit ambitious if you have limited rehearsal time, but Black Comedy would fit - there's a tremendous amount of physical comedy in it, especially for the lead.

We had a similar guy some years ago.  To showcase his talents during his senior year, we produced the musical Me and My Girl.  It's an old-fashioned British musical comedy with a true star-part male lead who needs to sing, dance, clown, and charm.  We did announce to the troupe that this role was pre-cast, but that all other roles were open.  He was predictably spectacular, and we had great experiences with the show.

Nice follow-up ... He fell in love with his leading lady.  After college, they married.  At their wedding reception, in a side room, they had an exhibit of photos and things from the show to let people see how it all started for them.  Today, he's a college English professor, she's a television news reporter and anchor, and they have a lovely daughter.  Who says real life never has happy endings?

When you say Dick Van Dyke, my first thoughts are obviously Bye Bye Birdie and Mary Poppins, if you haven't done these shows already. "Oscar Lindquist" in Sweet Charity is a great comic role, with wonderful improvisational opportunities. Catch Me If You Can has two strong male leads. I hope this is helpful.

What about "Anything Goes"?  There is Billy and Moonface. Especially if he sings and dances, cast him as Billy!  I second "Mary Poppins" if he is Dick Van Dyke-like.  You could do "Degas C'est Moi," its a one-act by David Ives.  Fantastic for a lead!  I've seen it done with an ensemble who use physical acting to be the setting.  You can cut down "Leading Ladies" by Ken Ludwig into a one act.  The father in Steve Martin's "W.A.S.P." is great, too.  Or the lead actor in Durang's "Actor's Nightmare." 

Addams Family - yes, the role of Gomez (played by Nathan Lane). That started me thinking on other Nathan Lane roles...Bialystock in The Producers, Pseudolus in Forum, Nathan Detroit in Guys & Dolls.

Title role in Batboy.

A couple of shows that worked for me when I was blessed to have this kind of actor.... CRAZY FOR YOU, THE MUSIC MAN, CURTAINS, ADDAMS FAMILY (Gomez), DIRTY ROTTEN SCOUNDRELS (Freddy) and ME AND MY GIRL.

I have one of these students now, and I have had a blast working with him.  Three musicals that worked well for his comic triple-threat skills were Urinetown as Bobby Strong (not much dancing, though) Addams Family as Gomez,  and Big Fish as Edward.  That show was a tour de force for him, and an amazingly comical yet heartfelt story.  Outside of our school, at a local youth theatre, he also played Leo Bloom in The Producers which was amazingly well received and acted - but it's still not a high school appropriate show.  

Another two shows I've done that really highlighted a comical triple-threat are Curtains and Drowsy Chaperone. Drowsy has a lead requiring amazing acting skills, and a featured lead that's a triple threat.  

Enjoy your time with your student!  Mine's off to Northwestern!

I would echo Anything Goes.  The role of Billy is so perfect for this type of actor.  Plus you have tons of roles for everyone else, including your triple threat girls.

I would echo Crazy for You! Its wonderful and expandable. Has lots of fun group scenes where your chorus really gets a chance to be a part of something. One of the first musicals I ever did with my current program - while it was still finding its feet- and its still held in high regard by our community. 

Don't you just love years when you have a triple threat?

That will be me next year as well, but with a female. Regarding your question, I would echo the comments about Mary poppins, or Crazy for you. Maybe add leading player in pippin, producers, or Ren in Footloose, Just some thoughts. Good Luck!