Is your current design just a PWM to a FET in order to turn on and off the LED? What, if anything, are you using for current control?
For something in the multi-watt range, you probably want to use a standard buck (or boost) topology, which means you are controlling your PWM circuit based on current through the string and the current in the inductor. While a linear CC driver is possible, your efficiency is pretty terrible unless you can very closely match the input voltage to the needed LED voltage (+offset).
You can save yourself a lot of heartache (and broken LEDs) if you use an existing buck controller, which are quite cheap these days. An NCP3066 is a cheap option, and has a built-in PWM control input. Depending on how the LED chip is made (series, parallel), the LM3404 (HV) can also drive high voltage 1A series strings.