Nah I'm not seeing the King's position being popular with the public, not with 1930s attitudes. You are under-estimating the level of religious belief at the time, 60/70% of the population are church members of one sort or another and ~50% believe the "anointed by God" part of the coronation ritual has a deep and real spiritual meaning and significance. On top of that there is pride in the Empire, once it comes out that the Dominions are against it that is another nail in Eddies coffin. Some sympathy for him as a man, perhaps, but not for him as a King.
Baldwin did not get to the top and stay there through the Depression by being an idiot. He knows how to read the public and play the press. He will not lead with "Yes, but". The response will be something like "The government, together with the opposition, the governments of the Dominions and the major church leaders, have reluctantly concluded that they cannot support the King's choice in this matter. It would be incompatible with his coronation oath and his duties to the country, to the Empire and to God. The Prime Minister has resigned, the opposition leaders has made it clear he will not serve, and we all beseech his majesty to reconsider and follow the example of his illustrious father in putting the needs of his people and his Empire first in his considerations."
Really lay it on thick about how Eddie is abandoning the country and his duties by being a selfish idiot. Throw in as much stuff about religion as the Archbishop of Canterbury will let you get away with and a reference to KG V (who is still deeply popular) and just absolutely hammer him hard.