That move was shortly following Doolittle's raid -- which was more jarring to the Japanese mythological psyche than the Pyrrhic win in Coral Sea or the disaster of Midway. The attack on the home islands is what eventually brought forth the image of the Divine Wind, and its modern implementation to defend against the ancient threat twice avoided by that means).
I don't know what "mythological psyche" means, but the sources I know indicate that the Doolittle raid made little impression on the Japanese people in general. In The Second World War, John Keegan writes (page 271): "The citizens of Tokyo, to whom no public acknowledgment of the raid was made by the government, did not associate the scattering of explosions with an American attack." John Toland, in But not in Shame (page 362) says: "Since little damage was done, the raid caused no panic."
The generals and admirals like Tojo and Yamamoto used the fact of the raid to push for a decisive naval battle with the US—which led to Midway. Nonetheless, it would be difficult to argue that the Doolittle raid helped push Morihei to move to Iwama. It presupposes knowledge he did not in fact have.
The Doolittle raid mattered more in boosting the battered American psyche, but its effect on the Japanese mind was slight.