One of the first problem we have to solve is to determine where the transition between circulating and librating orbits actually occurs.   We already know that this happens inside the libration island, as found in the secular problem.  The following two figures reports the results of two simulations with initial conditions close to this boundary.  The first show the final state of 21 particles whose initial conditions were chosen with the following criterion: I first performed a simulation of 1000 yrs with S2000/S5 and the OSS and determined the values of \Omega, \omega, and M that the satellite had when e=e_Max.  These were:

We used those values of the angles for all 21 particles.  The semimajor axis was the average value of a of S2000/S5, and the inclination were assigned values of inclination starting with 40.0^o and a
step of 0.1^o.    The second simulation show the end state of 31 particles with same initial conditions, but with initial inclination starting from 41.2^o and a step of 0.01^o.   The figures report the fate of the particles, and the limits of the librations island according to the secular problem.   Red dots represents particles that remained in the libration island for the length of the simulation, black dots particles that were circulating, and blue dots particles that alternate libration to circulation.   The second set of initial conditions adequately determine the lower boundary of the transition region.
 
 

Finally, to set up our simulations with filtered elements it is useful to know what the period of \omega precession is for particles in and out of the libration island.  The following plot report such period (numerically determined) as a function of initial inclination.

As can be seen from the plot, the precession period of \omega goes from a minimum of 400 years to a maximum of 1300.  This corresponds to a range in frequencies of 990-3240 "/yr.   We therefore choose to sample an interval in frequencies that goes from 700 to 4000 "/yr.