Any pros and cons on relocating register on the ceiling?

I need to relocate a Heat/AC register (Labeled 2)

I am planning to move it to new location (Labeled 3), kind of in the middle of the room on the ceiling.

At the same time I think I need to move the bathroom fan from (Labeled 1) to new location (Labeled4) in order to better cover the shower area where the humidity will be.

I know that the new location of the register is not ideal but I do not have another option.

Do you foresee any issues with this plan ?

The only other possible option would be to install it on the wall that is behind the viewer but since the duct is 4" in diameter it wont fit in the internal partition wall that separates the bathroom from a hallway.