I have no idea how that method works, not having a copy of the book. However, I have used a step wedge to test paper in the past and getting 3 steps before you start to get some tone and then not going black long before it reaches step 21 suggests a major problem somewhere. Some possibilities occur: are you leaving the print to fully develop? Fibre will want at least 2 minutes in most developers, 3 or 4 minutes in some (especially warm tone developers) would not hurt, and is the developer fresh?
How large an image are you projecting on to the paper: that may explain the long times. You don't really need more than about x2 magnification which should be only a few seconds, even with a diffusion enlarger.
I put dots on the wedge alongside the steps to make it easier to see where each step is later.
Good luck, Bob.