You have the right idea. You won't need to bring the wort to a boil though. Bring it up to about 180°F then stir in the LME. Hold it above 175°F for about 10 minutes. Pasteurization occurs at 171° in just over a minute. Cool to yeast pitching temperature, aerate in the kettle, and then add to the fermentor. Be sure to cool to yeast pitching temperature of about 60° to 65°F.
You can pitch your yeast while the enhanced wort is cooling.
Remember to sanitize during the pour.
EDIT: Cool to within 5° of the temperature of the wort in the fermentor.