A mink is the only predator that has ever killed any of my poultry (despite having raccoons, possums, coyotes, eagles, hawks and owls all around), and I think you are doing things right. I added Nite Guard solar-powered blinking lights after the massacre. I've been told that they don't really deter minks, so maybe it's coincide that I haven't had any more losses.
Once a mink attacks, it will come back. Well-secured hardware cloth on and in the ground around your runs makes attacks less likely.
One bit of good news I discovered in my research is that if the mink is a male, it will have its own territory and won't allow other males in. So, you may only have to deal with one.
Best wishes keeping your birds safe.