The experts tell me to transfer--no matter what.

I believe the odds favor more tricks ( or fewer set tricks)  in 3Major  than remaining in 2NT.

      The only way you can get some tricks out of that 5 card Major is to make it the trump suit.     The  risk is getting to a 4M contract ( when you wanted to "get out" in 3M ) if Opener "super accepts" with a max and 4 card support.

      Certainly having a stiff or void increases your chances of actually making the contract.

I am no expert  but  I learned the same as Twofer 

Love your picture