There's a nice general lesson from double cruxing that you can apply outside of one on one arguements if you care about holding consistent beliefs.

Always argue for your weakest crux. I.e. out of all the necessary premises of some position you hold, always keep the hardest to defend premise close to the front of your mind.

This is counterintuitive because people reflexively try to bury their weakest assumptions. What's more: we're rewarded for presenting strong arguments. But if there's some fact that, if disproven, would cause you to change your mind and you aren't really confident that that fact is true - you should care the most about finding out if it's false, or at the very least becoming more certain in your belief about it.