I overcame the same "problem" not by progressively increasing my speed, but by working to refine my technique (which I largely learned from books and videos) at a modest speed. I practiced looking through turns, deliberate counter steering, taking exactly the line I wanted to, shifting my weight, being super smooth on all the controls, etc.
I think some of my best practice came from times I when I was "stuck" behind a car going slow on a twisty road. Being forced to go slow meant I stayed well within my comfort zone, so I could focus on improving my technique. Picking roads with constant tight turns was also great practice (Mines, Mt. Hamilton, Diablo, Calveras, everything that branches off Skyline). As I became more confident that I could make my bike do exactly what I wanted, I found I was also going faster without really thinking about it.
FWIW, I still sometimes find it enjoyable to go on rides where I am focused on technique rather than pushing the speed envelope, sort of like what is described in the article "The Pace."