Aida really only has 3 solo male parts... if the rights are out...
In Bye, Bye Birdie, Albert and Conrad are the only males that actually have to sing solo... I mean, Mr. MacAfee does, but it can be mostly spoken and sound fine.
Oh, and Harvey Johnson, but his voice is supposed to be changing anyway
In Evita, only Che, Peron and Magaldi have to sing solo. But I suppose Magaldi isn't supposed to be FABULOUS...
Only Harold Hill and Marcellus sing completely solo in The Music Man, but you must have 4 boys who can sing nicely in barbershop quartet harmony.
And you have to have a cute little kid for Winthrop, but I don't know if you'll use an elementary-school kid like we always do.
I'm thinking Bye Bye Birdie is your best bet. Really cute show and can probably be done pretty well under your circumstances. I take it you have quite a few more talented girls than boys, and for Bye Bye Birdie, that's not a bad thing!
Hope that helps!