A solid state lighting device may include a power supply, a light emitting device, and a boost converter. The boost converter may have an input node electrically coupled to the power supply and an output node with the light emitting device electrically coupled between the output node and a reference node. The boost converter may include a switch electrically coupled in a current shunting path between the input node and the reference node, and a controller. The switch may be configured to shunt current from the power supply around the light emitting device. The controller may be configured to generate a pulse width modulation (PWM) signal to control a duty cycle of the switch to provide a pulse width modulated electrical current through the switch and a continuous electrical current through the light emitting device. Related methods are also discussed.