Sorry man, just saw this.
Yes, chlorophyll is water soluble, and less so in oil.
http://www.foodandnutritionjournal....erature-in-color-changes-of-green-vegetables/
Temperature control is one of the major treatments for increasing the time of their commercial life and maintain their quality. Cantwell et al (1998), reports that temperature is the only factor that determines the post-harvest quality of leafy green vegetables. It should be noted that the higher the storage temperature the faster the deterioration and the shorter the duration of the commercial life and this is because temperature affects the metabolism and respiration rate.
There's more there to dive into, but it seems like exposure to warm, dry temperatures before cooking will reduce the amount of chlorophyll that comes out. Maybe putting the buds in a dehydrator for a while or in front of a sunny window before cooking would also lessen the amount that gets picked up?