I personally have never used a technique in screen printing that would require a gradient, other than using the bitmap/photoshop technique. However, as it is a smooth and subtle gradient, it would be best to just place the ink straight onto the screen and drag to create different kinds of gradient, then choose which one would be most effective as the cover.
This gives many more options when entering a feedback session for example. People would be able to select the prints they think are of the highest quality and colour that best suits the song.
There is a process called 'Split Fountain' used within screen printing that enables you to use a single screen to achieve a multiple colour print. The video below has supplied me with all of information needed to achieve this effect within practice:
Credit: Level Press (https://www.youtube.com/watch?v=YMNhhp3GlWM)
There are a few pitfalls with this process however. Only a linear gradient can be achieved, so, if you were to create more of a displaced gradient like in the visual research post, it would require two separate screens that were processed through Photoshop's bitmap procedure the desired effect. This will make the job slightly harder as this means exposing two screen instead of simply grabbing a single screen, taping off the area and creating whatever gradient the screen felt like creating. This is still something to consider if the dual screen solution does not turn out the way intended, it is satisfying to know there is a safety net if the gradients do not come out as hoped.