Reshaping textures... through Blender?

Hello all. I’m writing this just before bed, so please excuse me if I ramble a bit.

Some time ago I created a very simple projection (a Butterfly Map variant) of a fictional world, but I’ve always wanted to reshape it into something more aesthetically pleasing. I’m hoping that I can do this by using Blender and have started the process.

Right now I have a UV sphere, on which I have marked seams and which I have unwrapped. I am now moving the vertices of the UV to coincide with the longitude/latitude lines on my fictional globe projection. When that’s finished I’ll have a nice 3D version of my world in a proper globe shape (rather than the octahedron that the original image makes).

Next is the bit that I’m not sure about.

I’d LIKE, if possible, to project the textured UV sphere into another style. To be able to unwrap it again, so that the UV map has a better shape, but keep the texture that I’ve applied.

To put it another way, I want to be able to map my current Butterfly Map onto a UV Sphere (already partly done) and then use Blender to create, for instance, an Equirectangular or Goode Homolosine image. For an explanation of such projections see wikipedia:

Is this possible? Any advice would be welcome!

you can do this via BI baking…

pretty much the overview is
make sure the texture is part of the shader applied to the object in BI, set up a second uv map with the uvs you are wanting, assign a blank texture to it & make it the uvs active, bake only textures.

Excellent! I’ll have to read a bit more to find the details of how to do those things, but that’s no problem! Thank you very much!

Absolutely spot on! UV mapped, and baking in any layout I assign to the second UV.