For Supporting Actor in a Musical, Chester Gregory will probably get the nod, over Shuler Hensley.
I'm not certain that Drowsy's score is its best feature. The critics in L.A. didn't go wild over the songs, though they found them generally pleasant. Drowsy's book was well received, but I think Jersey Boys still is the one to beat in that category.
I also think John Lloyd Young might just have a lock on Best Actor in a Musical.
Begin at the beginning and go on till you come to the end: then stop.