I see how I got confused. I remembered that when VirginiaTam in a recent thread suggested this game under the name "Song Title Turnover" such little connector words were disallowed, so I discounted them here.

You could get from Never on Sunday to I'll Never Say 'Never Again' Again as sung by Nat King Cole (as well as two singers listed in the thread linked from the song title) following VirginiaTam's rule to "exclude common words like: A, An, It, Me, Mine, My, On, One, That, The, There, This, You".

Thence, a couple of items from Mooh's Blues Christmas thread:

Christmas Is Here Again - Little Johnny Taylor
White Christmas -The Beatles

... Which gets you to White Sport Coat, with Marty Robbins.

From there (I'd Like to Get You on a) Slow Boat to China, but for now it's Goodbye, Fare Ye Well. Can you get to China yourself via only major words from song titles?