Wolf, Ram, and Hart, I am an admirer of yours, and will try my best to help you.
But you are speaking with such a thick “artist” accent that I am having trouble understanding what you mean by “straight around symmetrical and blended mapping”. I, in return, may be speaking too much “math” for you. Let’s see if we can converge.
I’m also wondering if you’re using “UV Map” when you mean “texture map”, because you mention PhotoShop and UV maps, but UV maps aren’t a PhotoShop capability. The texture map is the flat image (JPEG, PNG, TIFF, HDRI, etc) that gets wrapped around an object, the UV map is the table that translates the 3D coordinates of the object to the 2D coordinates of said picture. A program called an “unwrapper” tears apart the 3D mesh and creates UV map. For a sphere, you don’t need a sophisticated unwrapper, the cylindrical or cube unwrappers built into the free “UV Mapper” program can do what you want (it sounds paradoxical, but avoid UV Mapper’s “spherical” mapping. That actually is a pseudosinusoidal “orange peel” map that is a fracking pain to heal the seams). Just make sure your sphere is a relatively high polygon object, or you’ll get even more distortion and difficulty healing the seams.
What you described sounds like a major problem with seam healing. Can you show us the problem? Is it alignment, or is it brightness or color not matching.
There are many ways to UV map a sphere. Do you want to be able to “paste” a flat image onto the texture map and have it wrap around the sphere in a civilized fashion? Are you hand painting? The most common mapping for things like sky domes is “cylindrical projection” (which is also available on UV Mapper, so it’s handy). A cylindrical projection only has one seam (very easy to deal with, but if you don’t, look out, because it’s major) but is only reasonably distortion-free near the horizon. Distortion increases towards the top (zenith) and bottom (nadir) of the sphere, and at the zenith or nadir themselves, distortion is infinite, so they are very difficult to hand edit. They are a piece of cake to piece together out of multiple overlapping reasonably flat (conventional) pictures of a sky, if you use a panoramic stitching program. The one I normally use for this stuff is called hugin, and it’s a wrapper around a bunch of good programs (“enblend” and “enfuse” that blend pieces of sky or horizon without ugly seams, “panorama tools” to do the actual warping, “SIFT” and other automatic alignment programs).
Hugin supports every major mapping, but you want to use cylindrical or cube for this, matching whichever you chose in uv mapper when you unwrapped the sphere. Cube is a little easier to hand paint than cylindrical, but it’s also more likely to show visible seams. Everything wrong with the Worldbase product stems from a foolish choice of a cube map over cylindrical.