  Axisymmetric disks of high eccentricity, low mass bodies on near-Keplerian
orbits are unstable to an out-of-plane buckling. This "inclination instability"
exponentially grows the orbital inclinations, raises perihelia distances and
clusters in argument of perihelion. Here we examine the instability in a
massive primordial scattered disk including the orbit-averaged gravitational
influence of the giant planets. We show that differential apsidal precession
induced by the giant planets will suppress the inclination instability unless
the primordial mass is $\gtrsim 20$ Earth masses. We also show that the
instability should produce a "perihelion gap" at semi-major axes of hundreds of
AU, as the orbits of the remnant population are more likely to have extremely
large perihelion distances ($\mathcal{O}(100~\rm{AU})$) than intermediate
values.
