Hi! Here's what I think would work: cover your lips (including that pigmented edge) with a dab of foundation/concealer before applying any lip colors. That will create more of a blank canvas so you can literally draw on any lip shape you want with the liner, fill in your lips with the liner too, then blend it to a consistent color using a lip brush. You can also use the brush to "blur" the edge of the liner and soften the look, so it won't look so liner-y and precise.
The foundation/concealer will also help prevent bleeding too.
Let me know how that works for you!