I use "tap to click", so when I'm performing a click-and-drag, I tap-tap-drag. If my finger reaches the edge of the touchpad and I still need to drag the cursor farther, I quickly lift and place my finger closer the center of the pad so I can continue dragging. As long as I replace my finger on the touchpad quickly enough, it doesn't treat the finger-lift as the end of the drag-and-drop action.
This has worked for me on other distros. I had NixOS w/Gnome installed on my current machine before installing Ubuntu Gnome on it, and it worked, but I can't figure out how to make it work on Ubuntu.
Is there some hidden setting I need to configure?