Hi, I understand what you mean. You can do this, instead of sliding vertices or using the cut tool you can just delete faces and then extrude them. After that you can press F to make a whole new face at the tip of the extruded pipe.
Lowering the number of vertices in a circle also helps at the start, right after you put in a circle into the scenes press T to bring up the transform tool bar and under “Add Circle” you can limit the vertices. In the render below I had it at 8 which seems a bit too low, so something higher might work better. Having less vertices makes it more manageable. I’ve attached a blend file, you can explore that if you want.
A thing which helps a lot is how you view the object in the viewpoint, press 5 on your numpad to toggle between orthographic view or perspective and use the other numbers to switch between sides.
Share1.blend (511 KB)