My process is pretty much the same as above. Rinse well in very hot water, or soak in a glass of vodka overnight if the previous flavor is still hanging around a bit.
I do have one other tip that works for me. After I dry everything off, I wrap some paper towel around the replaceable head and lightly press some paper towel against both ends of the wicks for a few minutes. The paper towel will pull some of the water out of the wicks, resulting in a slightly better tasting vape after refilling with eliquid. I could probably just let the replaceable head sit for a while and let it air dry, but usually I don't have the patience for that.