rwjackson,
Darn. I haven't knowingly read the paper, but hoped that it would have shed some light on this topic. Perhaps you can query Ensoft. They have been helpful with me before with support for LPILE.
However (proceed at your own risk here, as I'm basically looking at this for the first time), based on the text presented in the Tech. Manual, the p-y curve for weak rock is based on a wedge failure (page 3-84). I will posit that this failure wedge is similar to that developed for clay (page 3-15).
From Eq. 3.89, Pur is a function of the diameter of the element, the compressive strength of the rock, a strength reduction factor based on RQD, and the depth of the layer below the rock surface.
K_ir and k_ir are both defined by the depth below the rock surface and the element diameter (Eqs. 3.91, 3.92, 3.93).
It seems likely that k_rm (within the range previously stated) is simply a fudge factor that controls the curvature of the p-y curve between the initial "elastic" portion and the limiting value of Pur.
You could construct the p-y curve based on your data and the equations in the manual in a spreadsheet and plot the resulting curve on the screen. Vary the k_rm value and see what effect it has on the curve.
Hope this was helpful,
Jeff