Mescaline in its naturally-occuring salt form(s) is water-soluble. Freebase mescaline is not.
Yes, you can let the tea sit for a while and some sediment will settle to the bottom. If the boils were thorough this sediment will contain a negligible amount of mescaline, if any at all. The vast majority of mescaline will be dissolved in the liquid solution.
I don't think naphtha would be very useful for the purpose you have presented.
I second mew's recommendation of using a pressure cooker. This drastically reduces the length of time required for the initial water extraction. Just boil the cactus with water for a while before pressure cooking, stirring periodically so it doesn't burn, and most of the snot will boil off.