Drywall – How to tape new drywall that is butted up against a textured wall

The point of Green Glue is to create a flexible layer of never fully firm glue between layers of drywall, right? To absorb sound?

In which case, I think you'll need to first level the ceiling, then apply green glue, then apply your final layer.

Otherwise, if you green glue over top of the texture, you'll have high points in the texture that touch the new layer of drywall. That will transfer sound quite effectively - which you don't want.

I never tape anything and people are amazed at the crisp lines I paint in my home. I use a high quality angled brush for this. Depending on my wrist fatigue and room, I work from either left to right, or vice versa with this technique. This is self-taught and I have no idea if their is a name for this.

I load the brush up with plenty of paint and then spread the paint on about an inch lower than the ceiling, onto the wall for about the length of a foot. This is just to get the bulk of the paint onto the wall to prevent dripping and to help load the brush back up while I work. I pull the brush along the wall just below the ceiling and slowly raise it up to the corner so that the bristles fall in to place. Without the angled brush, this would be difficult. I hold the brush more on plane with the ceiling than the wall, almost perpendicular to the wall. Once the bristles have fallen into a nice setup, most people would simply drag the brush and paint the wall with a one long stroke. I found that I run out of paint and have to use multiple shallow arcs to do this. This was unsatisfactory to me. I wiggle the brush back and forth while dragging it along to drag and push the paint to the place I want. The key of this method is to control the amount of paint loaded up on the brush at the ends while you drag and push. With the push and pull action of this method, I think it would work wonderfully for a textured surface as it pushes paint with both strokes in each direction

Upon very close inspection, the finished edge will have a small ragged appearance to it, but you can only see it when you are very close up. From normal viewing distance, even in a small bathroom, the line appears to be a crisp edge, well-defining the corner. I will be painting a room in the next week or two. I could take a quick video and post if it would be beneficial to anyone.

Edited to add video:

Video