Do small hive beetles overwinter inside the cluster, and is a beetle trap still earning its place in October?

North Carolina, third year, six hives. Beetles were a proper nuisance in August — I had traps in every hive and was still squashing adults on the inner cover every visit. Now that nights are in single figures the numbers have dropped right off and I've only found two beetles in the last fortnight. What I don't understand is where they go. I've read they overwinter as adults inside the cluster, warmed by the bees, which sounds grim but also means the ones in my hives now are next spring's problem. If that's true, is it worth pushing hard on traps for another few weeks, or does trapping in a cold hive just give me something to fiddle with while the bees are trying to settle? Related question — any autumn practice that reduces the spring beetle load? I've heard that beetles pupate in the soil and that keeping the ground under the hives dry and in the sun helps, and that reducing colonies to the space they can actually patrol is the real control. Interested in what works for people further south than me too.