It is an interesting problem, from my experience the capsaicin behaves in a way which is consistant with it being a liphilic substance. I know that if you fry chilli pueppers with some cheese that the cheese helps to bring out the flavour of chilli peppers.
I know that anacdotal evidence suggests that a dairy product such as milk or yougurt helps to stop your mouth burning. I think that this is reasonable if we assume that the chilli pepper toxin dissolves in the fatty droplets in the milk or yogurt. This might make it a better mouth decontamination liquid than water.
I think that the way to test this would be to put known amounts of capsaicin on filter paers and then soak them in milk and water and then measure the capsaicin concentration in the liquids after soaking. It could be done with HPLC or if we were able to get C14 labled compound we could use liquid scintillation counting.
From my student days I recall that a vegatarian or sasuage chilli was hotter than one made with minced beef. So it is possible that the capsaicin adsorbs onto the surface of the beef. Maybe you should consider using the langmuir isotherm to model such a thing.
As a simple alternative just put less chilli in the food.