Can overshoot current from DC/DC converter damage LED lamp?
The problem is in your control loop.  This is the firmware that senses what the supply is doing, compares that to what you want it doing, then adjusts the PWM duty cycle as a result.

You haven't said anything about your control loop, so there is little we can say about it either.  In general, it is too aggressive.  In your situation it seems that slow response to a new situation isn't a big deal.  LEDs are pretty fixed in their characteristics.  You can therefore overdamp the controller.  That will greatly reduce or eliminate overshoots, at the expense of slow transient response.

There are whole books on how to optimize control loops.  However, fancy control schemes are often not needed.  I'd use a simple pulse on demand system.  When the output falls below the regulation threshold, you do a pulse, else you don't.  This has more ripple, but is nicely stable with no more overshoot than what a single pulse can produce.

This is exactly the control scheme I used in my KnurdLight LED headlamp.  The control scheme is so simple it runs in a PIC 10F.