Does dairy-based marinade increase the amount of browning (Maillard reaction) in meats?
Two things that encourage Maillard reactions are more heat and higher PH. Modernist cuisine has instructions to caramelise food in water using a pressure cooker and baking soda. Baking soda can taste soapy. You can also look to non-flavored antacid from the chemist and something used in asian noodle making called alkaline salts or lye water.