Wizkids Rules!

The ability text reads

If God Emperor Doom is blocked by 4 or more character dice, return the blocked die to its card.

When does this effect actually occur? Does it happen immediately after all blockers are declared or is it at the end of the attack step after damage is dealt (assuming he would return to his card regardless of if he survived or not)?

If the former, I presume that would mean that the dice blocking him are still spoken for and cannot switch to block a different die.

If it's the latter, could you theoretically use some ability during the global window that spins/rerolls him to an energy face and save him from having to go back to his card (since he would technically no longer be on the field and thus not actually blocked anymore)?

This ability is resolved in the Declare Blockers sub-step of the Attack Step and is treated as a “when this Character die is blocked” effect. The Character dice assigned to block God Emperor Doom cannot be switched to block a different Character die, unless an ability allows the switching of blockers, e.g. Brainiac – Twelfth-Level Intelligence:

While Brainiac is active, after blockers are declared, you may switch two opposing blockers.

Refer to Rule 2.7.2.5:

After all blockers are declared, resolve any abilities that occur due to character dice blocking or being blocked, such as “when this Character die blocks”, “when this Character die is blocked”, or “when this Character die is engaged” before proceeding to the next sub-step.