I currently can't sphere/cylinder map this type of chart/cuts

[micheus]

I should have made all the image steps...

I didn't say you need a real straight line.
That red line is representing the two sides (left an right) of the texture when you roll it in a cylinder. The point where they are "glued".

The Black line is just the right boundary of the your UV map "mesh". The oder left side is laying in the right side of the red line and I didn't represented it. But it's there.

The space between both is what is causing the noise you see in that sub dark image. It's a portion of your UV mapped sphere.

So, if you really "allow UV to go to 1.01...", but also -0.01 - something you are not doing - you will remove that noise and you will get your sphere perfectly mapped - no gaps or noise in the result produced.
Think that as scaling the UV in the horizontal until that sinuous black line be centred in the imaginary red one - some vertices will lay on the left of it other on right.

But, it's of your interest this, not mine. I don't know why I keep trying to explain this kind of stuff. It's a bit of compulsive.
I need to take control over this otherwise my precious time to work in Wings3D flies away.