That simulation window is not including the current step. Change "For" to 4000 ms, "after reporting delay of" to 8s, and the step current on the current sink to kick in at 10 seconds. That will get you a simulation window that starts at 8 seconds, gathers data for 4000 simulation milliseconds, and steps the current right in the middle of that window at 10s. You may also need to change the value of the current step to be more like 300 mA to be able to see what happens.
With a DCR of 84 ohms on the transformer secondary and 300 ohms on the choke, all the ringing will be well damped out. (I assume those DCR values are accurate.) To see the ring frequency, temporarily change your choke DCR to something like 50 ohms and your transformer secondary DCR to 31 ohms, resimulate and you will be able to see the ring frequency on V(C2) by zooming in on the current step (use mouse to select zoom area; can select multiple times to zoom in tighter and tighter). I popped this into my copy of PSUD and I can see that the ring frequency is right at 6Hz, so your calculation is accurate. Note that calculation does not give you the amplitude of the initial overshoot. There's probably a formula for it but it's just as easy to simulate. With your current setup, the resistance in your circuit well over damps the resonance, and you have a nice smooth transition between low and high currents. Looks good.