Shifting an equirectangular map north/south

[acrosome]

Here I have a fine world map:



It is Venus, churned through Wilbur and rotated 180 degrees (for reasons).

Let's say that during the terraforming process the planetary engineers stopped Venus's rotation, and then later re-spun it but on a slightly different axis. Is there software out there that will let me manipulate this image to change the axis of rotation? Sort of shift everything north by 15 degrees, while appropriately deforming things to keep the equirectangular projection?

Actually, I would want to do this with the original Venus grayscale heightmap. But is there a straightforward way to do this?