—“What’s the relationship between truth-telling and dueling? Is it because you should only say something you believe to the extent that you’re willing to fight for it?”—
Great question.
It’s actually two different issues.
You impose a cost on someone else’s reputation at the peril of your life. Especially after guns were invented. They are a great equaliser.
If you speak truthfully and it imposes a restitution then that is a moral obligation to your fellow citizens.
If you speak the truth in general then that is a cost to you but it is the cost of entry into the informational commons just as respect for property is a cost you must bear for entry into the market.
The purpose of judicial combat was to create time to cool off and apologize, and negotiate a settlement rather than put noble families in feud.
The duel degenerated into sanctioned murder. The problem is preventing duel by construction (murder).
That requires a third party to judge the restitution for the insult.